{"id":33873,"date":"2023-09-07T15:22:00","date_gmt":"2023-09-07T15:22:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33873"},"modified":"2023-09-11T02:47:18","modified_gmt":"2023-09-11T02:47:18","slug":"circumscribe-in-math-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe","title":{"rendered":"Circumscribe in Math: Definition with Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-fbcdbf32-6d79-424f-9a94-e2a7272fddc1\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe#0-what-does-circumscribed-mean-in-math>What Does Circumscribed Mean in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe#3-steps-to-construct-a-circumcircle-of-a-triangle>Steps to Construct a Circumcircle of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe#9-circumscribed-vs-inscribed>Circumscribed vs. Inscribed<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe#12-solved-examples-on-circumscribed-shapes>Solved Examples on Circumscribed Shapes<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe#13-practice-problems-on-circumscribed-shapes>Practice Problems on Circumscribed Shapes<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe#14-frequently-asked-questions-on-circumscribed-shapes>Frequently Asked Questions on Circumscribed Shapes<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-does-circumscribed-mean-in-math\">What Does Circumscribed Mean in Math?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A circumscribed shape means a shape drawn around another shape such that it is touching it at points (vertices) but not cutting it.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/shape\">shape<\/a> is restricted within another shape and there is no way for the inside figure to pass through the outer figure, then we say that the inner shape is circumscribed by the outer shape. The outer shape touches the maximum number of points of the shape inside without crossing it.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To circumscribe means to restrict someone\u2019s or something\u2019s freedom. The prefix \u201ccircum\u201d means \u201caround,\u201d and \u201cinscribe\u201d means \u201cto be within the boundaries of.\u201d&nbsp; Thus, \u201ccircumscribed\u201d means a shape is drawn around another shape.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1: Circumscribed hexagon<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, a hexagon is drawn around a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/circle\">circle<\/a> touching the maximum number of points on the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/circumference-of-a-circle\">circumference<\/a> but not crossing it.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-hexagon.png\" alt=\"Circumscribed hexagon\" class=\"wp-image-33877\" title=\"Circumscribed hexagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-hexagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-hexagon-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2: Circumscribed circle or circumcircle<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, a circle is drawn around a triangle such that the circle passes through all the three vertices of the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a>. This is termed the circumcircle of a triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"450\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle1.png\" alt=\"Circumscribed circle of a triangle\" class=\"wp-image-33878\" title=\"Circumscribed circle of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle1-300x218.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-circumscribe-definition\">Circumscribe: Definition<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Circumscribe means to draw a shape around another shape such that the outer shape touches maximum points of the inside shape but not crossing it such that the inside shape is enclosed or restricted within the bounds of the outer shape.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-circumscribed-circle\">Circumscribed Circle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The circle that passes through all the vertices of another geometrical figure or a polygon but does not cross it is called \u201ccircumscribed circle\u201d or \u201ccircumcircle.\u201d&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When a circle circumscribes a quadrilateral, the quadrilateral is called a \u201ccyclic quadrilateral.\u201d The sum of the opposite angles of a cyclic quadrilateral equals 180 degrees.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take a look at a square circumscribed by a circle. Here, the diameter of the square equals the diagonal of the square.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"415\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/a-square-circumscribed-by-a-circle.png\" alt=\"A square circumscribed by a circle\" class=\"wp-image-33879\" title=\"A square circumscribed by a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/a-square-circumscribed-by-a-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/a-square-circumscribed-by-a-circle-300x201.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Diagonal of a square $= \\sqrt{2}$ \u00d7 (side of the square) = $\\sqrt{2}$ \u00d7 s<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the diameter of the circle $= \\sqrt{2}$ \u00d7 (side of a square)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using this formula, you can determine the side of the square if the diameter of the circle is given.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Circumcircle radius = Radius of the circle $= \\frac{\\sqrt{2} \\times (side \\;of \\;a \\;square)}{\\sqrt{2}} = \\frac{side\\; of\\; the\\; square}{\\sqrt{2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-steps-to-construct-a-circumcircle-of-a-triangle\">Steps to Construct a Circumcircle of a Triangle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s understand the steps for constructing a circumcircle of a triangle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: <\/strong>Construct a triangle with the required angle measurements.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-i.png\" alt=\"Triangle ABC\" class=\"wp-image-33881\" title=\"Triangle ABC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-i.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-i-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2:<\/strong> Draw perpendicular bisectors of two sides of the triangle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-ii.png\" alt=\"Perpendicular bisectors of sides AB and BC of triangle ABC\" class=\"wp-image-33882\" title=\"Perpendicular bisectors of sides AB and BC of triangle ABC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-ii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-ii-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3:<\/strong> Label their point of intersection as O. Using O as the center and keeping OC as distance, draw a circle around the triangle touching all the three vertices or corners of the triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"429\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-iii.png\" alt=\"Construction of circumcircle of a triangle\" class=\"wp-image-33883\" title=\"Construction of circumcircle of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-iii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/construction-of-circumcircle-step-iii-300x208.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-circumscribed-triangle\">Circumscribed Triangle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A circumscribed triangle is a triangle that is drawn around another geometric shape in such a way that it touches the inside shape at maximum points without ever cutting it. Here, the triangle is the outside shape.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"361\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle.png\" alt=\"Circumscribed triangle\u00a0\" class=\"wp-image-33884\" title=\"Circumscribed triangle\u00a0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle-300x175.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The triangle in the above figure surrounds the circle in such a way that its sides are tangent to the circle. We can also term it as a circle inscribed in a triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-circumscribed-polygon\">Circumscribed Polygon<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A circumscribed polygon surrounds a geometric shape in a way that all of its vertices touch the boundaries of the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a> (regular or irregular).&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"360\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-polygon.png\" alt=\"Circumscribed polygon\" class=\"wp-image-33885\" title=\"Circumscribed polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-polygon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-polygon-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-circumscribed-quadrilateral\">Circumscribed Quadrilateral<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A circumscribed quadrilateral encloses a geometric figure in such a way that its sides pass through maximum points of the inside shape without crossing it.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The figure below shows a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\">quadrilateral<\/a> enclosing a circle. Here, the sides of the quadrilateral act as a tangent to the circle. Note that not all quadrilaterals can be circumscribed.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"413\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-quadrilateral.png\" alt=\"Circumscribed quadrilateral\" class=\"wp-image-33886\" title=\"Circumscribed quadrilateral\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-quadrilateral.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-quadrilateral-300x200.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">When a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\">square<\/a> circumscribes a circle, the diameter of the circle equals the side of the square.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, the square ABCD circumscribes the circle with radius a such that the side of the square = 2a.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square1.png\" alt=\"A square circumscribes a circle\" class=\"wp-image-33887\" title=\"A square circumscribes a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square1-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-circumscribed-hexagon\">Circumscribed Hexagon<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A circumscribed hexagon surrounds a geometric figure so that it passes through each vertex of the inside shape.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the given figure, a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/hexagon\">hexagon<\/a> circumscribes a circle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"372\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-hexagon-example.png\" alt=\"Circumscribed hexagon\" class=\"wp-image-33888\" title=\"Circumscribed hexagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-hexagon-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-hexagon-example-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-circumscribed-angle\">Circumscribed Angle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When the arms of an <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\">angle<\/a> touch the circle forming two tangents, the angle is said to be a circumscribed angle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"693\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/ciricumscribed-angle.png\" alt=\"Circumscribed angle\" class=\"wp-image-33889\" title=\"Circumscribed angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/ciricumscribed-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/ciricumscribed-angle-268x300.png 268w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-circumscribed-vs-inscribed\">Circumscribed vs. Inscribed<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A geometrical shape drawn inside another shape such that all its vertices touch the outer shape without crossing it, the inside shape is called inscribed shape. A circumscribed figure is a shape drawn outside another shape.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We have to first understand which figure we want to describe before using the terms circumscribed and inscribed.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the left image, we have an inscribed circle of a triangle.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(Note: We can also call this a circumscribed triangle.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the right image, we have the circumcircle, the circle circumscribes a triangle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(Note: We can also call this an inscribed triangle.)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"286\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-vs-inscribed.png\" alt=\"Inscribed circle vs. circumscribed circle\" class=\"wp-image-33890\" title=\"Inscribed circle vs. circumscribed circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-vs-inscribed.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-vs-inscribed-300x138.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-facts-about-circumscribed-shapes\">Facts about Circumscribed Shapes<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Circumscribing involves placing one shape around another so that the outer shape touches maximum points of the inside shape.<\/li>\n\n\n\n<li>They can be found in many geometric figures like triangles and circles.<\/li>\n\n\n\n<li>The circumscribed circle of a polygon is the smallest circle that contains all its vertices.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we learned about different circumscribed shapes. Let\u2019s solve a few examples and practice problems for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-solved-examples-on-circumscribed-shapes\">Solved Examples on Circumscribed Shapes<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. A square circumscribes a circle with radius of 10 units. What is the area of the square?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square.png\" alt=\"A square circumscribing a circle with radius 10 units\" class=\"wp-image-33891\" title=\"A square circumscribing a circle with radius 10 units\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-square-120x120.png 120w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The square circumscribes a circle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Radius of circle = 10 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diameter of circle = 20 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diameter of circle = Side of square = 20 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of square = side<sup>2<\/sup>= 20<sup>2 <\/sup>= 400 square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. The quadrilateral ABCD is encircled by a circle, as indicated in the illustration. Find the missing angles.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"297\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-circle.png\" alt=\"cyclic quadrilateral problem\" class=\"wp-image-33892\" title=\"cyclic quadrilateral problem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-circle.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-circle-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-circle-120x120.png 120w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sum of the opposite sides of a quadrilateral enclosed in a circle equals 180 degrees.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220A + \u2220C = 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">82\u00b0+\u2220C = 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220C = 180\u00b0 \u2212 82\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220C =98\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Similarly,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220B +\u2220D = 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220100\u00b0+\u2220D = 180\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220D = 180\u00b0\u2212\u2220100\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2220D = 80\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As a result, C = 102\u00b0 and D = 75\u00b0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-practice-problems-on-circumscribed-shapes\">Practice Problems on Circumscribed Shapes<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Circumscribe in Math: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">When a circle is drawn outside a figure in a manner that it is passing through all the vertices of the figure but not intersecting it, then it is called _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">circumscribed circle<\/div><div class=\"spq_answer_block\" data-value=\"1\">circumscribe triangle<\/div><div class=\"spq_answer_block\" data-value=\"2\">circumscribed polygon<\/div><div class=\"spq_answer_block\" data-value=\"3\">circumscribed rectangle<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: circumscribed circle<br\/>A circumscribed circle is a circle drawn around a geometrical figure.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which option correctly describes the given diagram?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-angle.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">a circle<\/div><div class=\"spq_answer_block\" data-value=\"1\">inscribed angle<\/div><div class=\"spq_answer_block\" data-value=\"2\">circumscribed angle<\/div><div class=\"spq_answer_block\" data-value=\"3\">right angle<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: circumscribed angle<br\/>The angle whose arms are tangents to a circle is known as the circumscribed angle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The given diagram represents a<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-octagon.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">circumscribed polygon<\/div><div class=\"spq_answer_block\" data-value=\"1\">circumscribed pentagon<\/div><div class=\"spq_answer_block\" data-value=\"2\">circumcircle<\/div><div class=\"spq_answer_block\" data-value=\"3\">Inscribed octagon<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: circumscribed polygon<br\/>This is a circumscribed polygon (octagon). It circumscribes a circle. <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the meaning of circumscribed shape?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A shape drawn around another shape<\/div><div class=\"spq_answer_block\" data-value=\"1\">A shape drawn inside another shape<\/div><div class=\"spq_answer_block\" data-value=\"2\">Both A and B<\/div><div class=\"spq_answer_block\" data-value=\"3\">None<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: A shape drawn around another shape<br\/>Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The fancy clock shown below represents a<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle-example.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">circumcircle<\/div><div class=\"spq_answer_block\" data-value=\"1\">circumscribed triangle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangle within a circle<\/div><div class=\"spq_answer_block\" data-value=\"3\">circumscribed clock<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: circumscribed triangle<br\/>This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Circumscribe in Math: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Circumscribe in Math\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"When a circle is drawn outside a figure in a manner that it is passing through all the vertices of the figure but not intersecting it, then it is called _________.\",\n                    \"text\": \"When a circle is drawn outside a figure in a manner that it is passing through all the vertices of the figure but not intersecting it, then it is called _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A circumscribed circle is a circle drawn around a geometrical figure.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumscribe triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A circumscribed circle is a circle drawn around a geometrical figure.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumscribed polygon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A circumscribed circle is a circle drawn around a geometrical figure.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumscribed rectangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A circumscribed circle is a circle drawn around a geometrical figure.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"circumscribed circle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A circumscribed circle is a circle drawn around a geometrical figure.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A circumscribed circle is a circle drawn around a geometrical figure.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which option correctly describes the given diagram?\",\n                    \"text\": \"Which option correctly describes the given diagram? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-angle.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The angle whose arms are tangents to a circle is known as the circumscribed angle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a circle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angle whose arms are tangents to a circle is known as the circumscribed angle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"inscribed angle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angle whose arms are tangents to a circle is known as the circumscribed angle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"right angle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angle whose arms are tangents to a circle is known as the circumscribed angle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"circumscribed angle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The angle whose arms are tangents to a circle is known as the circumscribed angle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The angle whose arms are tangents to a circle is known as the circumscribed angle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The given diagram represents a\",\n                    \"text\": \"The given diagram represents a <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-octagon.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"This is a circumscribed polygon (octagon). It circumscribes a circle. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumscribed pentagon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"This is a circumscribed polygon (octagon). It circumscribes a circle. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumcircle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"This is a circumscribed polygon (octagon). It circumscribes a circle. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Inscribed octagon\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"This is a circumscribed polygon (octagon). It circumscribes a circle. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"circumscribed polygon\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"This is a circumscribed polygon (octagon). It circumscribes a circle. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"This is a circumscribed polygon (octagon). It circumscribes a circle. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the meaning of circumscribed shape?\",\n                    \"text\": \"What is the meaning of circumscribed shape?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A shape drawn inside another shape\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Both A and B\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"A shape drawn around another shape\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Circumscribe refers to drawing a shape around another shape such that the outer shape touches the corner points of the inside shape but not crossing it. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The fancy clock shown below represents a\",\n                    \"text\": \"The fancy clock shown below represents a <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/circumscribed-triangle-example.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumcircle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangle within a circle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"circumscribed clock\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"circumscribed triangle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"This is a circumscribed triangle. A triangle has a circle inscribed inside. The triangle circumscribes the circular clock. We can also call this as an inscribed circle of a triangle.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-frequently-asked-questions-on-circumscribed-shapes\">Frequently Asked Questions on Circumscribed Shapes<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7301e7b8-40b2-4988-b1fe-1214c7e106a5\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-7301e7b8-40b2-4988-b1fe-1214c7e106a5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7301e7b8-40b2-4988-b1fe-1214c7e106a5\"><strong>What is an incircle of a triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-7301e7b8-40b2-4988-b1fe-1214c7e106a5\">\n\n<p class=\"wp-block-paragraph\">It is the largest circle drawn within the triangle. It is the circle inscribed in a triangle that touches the three sides.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-7301e7b8-40b2-4988-b1fe-1214c7e106a5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7301e7b8-40b2-4988-b1fe-1214c7e106a5\"><strong>Do all triangles and quadrilaterals have circumcircles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-7301e7b8-40b2-4988-b1fe-1214c7e106a5\">\n\n<p class=\"wp-block-paragraph\">All triangles have a circumcircle, but all quadrilaterals do not. A rhombus (which is not a square) cannot have a circumcircle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-7301e7b8-40b2-4988-b1fe-1214c7e106a5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7301e7b8-40b2-4988-b1fe-1214c7e106a5\"><strong>What is the meaning of inscribed shape?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-7301e7b8-40b2-4988-b1fe-1214c7e106a5\">\n\n<p class=\"wp-block-paragraph\">It means a shape drawn within another such that maximum points on the boundaries touch but the shapes do not intersect.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-7301e7b8-40b2-4988-b1fe-1214c7e106a5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7301e7b8-40b2-4988-b1fe-1214c7e106a5\"><strong>What is the circumcenter of a triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-7301e7b8-40b2-4988-b1fe-1214c7e106a5\">\n\n<p class=\"wp-block-paragraph\">The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of the triangle intersect.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Does Circumscribed Mean in Math? A circumscribed shape means a shape drawn around another shape such that it is touching it at points (vertices) but not cutting it. When a shape is restricted within another shape and there is no way for the inside figure to pass through the outer figure, then we say &#8230; <a title=\"Circumscribe in Math: Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/circumscribe\" aria-label=\"More on Circumscribe in Math: Definition with Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-33873","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=33873"}],"version-history":[{"count":5,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33873\/revisions"}],"predecessor-version":[{"id":33900,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33873\/revisions\/33900"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}