{"id":32398,"date":"2023-07-28T02:19:47","date_gmt":"2023-07-28T02:19:47","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?p=32398"},"modified":"2024-02-05T15:37:17","modified_gmt":"2024-02-05T15:37:17","slug":"point-of-concurrency-definition-facts-examples-practice-problems","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/point-of-concurrency","title":{"rendered":"Point of Concurrency &#8211; Definition, Facts, Examples, Practice Problems"},"content":{"rendered":"<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-0234cbae-c62f-4707-8c80-c7f7483078f5\" 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\/point-of-concurrency#0-what-is-the-point-of-concurrency-in-geometry>What Is the Point of Concurrency in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-of-concurrency#3-how-to-find-points-of-concurrency>How to Find Points Of Concurrency<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-of-concurrency#7-solved-examples-on-point-of-concurrency>Solved Examples on Point of Concurrency<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-of-concurrency#8-practice-problems-on-point-of-concurrency>Practice Problems on Point of Concurrency<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/point-of-concurrency#9-frequently-asked-questions-about-point-of-concurrency>Frequently Asked Questions about Point of Concurrency<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-point-of-concurrency-in-geometry\">What Is the Point of Concurrency in Geometry?<\/h2>\n\n\n\n<p><strong>The point of concurrency is the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/point\">point<\/a> where three or more <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line\">lines<\/a> intersect each other or pass through. In simple words, it is the point of intersection of three or more lines.&nbsp;<\/strong><\/p>\n\n\n\n<p>The word \u201cconcurrent\u201d refers to events occurring simultaneously or at the same time. In 2D geometry, concurrent lines are the lines that precisely cross at one point. The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/intersecting-lines\">intersecting lines<\/a> are always concurrent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency.png\" alt=\"Point of concurrency\" class=\"wp-image-32400\" title=\"Point of concurrency\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Lines l, m, and n intersect each other at point A. That means A is the point of concurrency. Lines l, m, and n are concurrent lines.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/fill-missing-numbers-using-decimal-point-patterns\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_placement_of_dec_point_pattern_pt.png\" alt=\"Fill Missing Numbers Using Decimal Point Patterns Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Fill Missing Numbers Using Decimal Point Patterns Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-distance-between-two-points\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/coordinate_distance_btw_2_points_pt.png\" alt=\"Find the Distance between Two Points Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Distance between Two Points Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-coordinates-of-the-point\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/coordinate_identify_coordinate_pt.png\" alt=\"Identify the Coordinates of the Point Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Coordinates of the Point Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/plot-multiple-points-on-coordinate-planes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/coordinate_plot_pts_on_graph_pt.png\" alt=\"Plot Multiple Points on Coordinate Planes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Plot Multiple Points on Coordinate Planes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/plot-points-using-patterns\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/coordinate_plot_pts_patterns_pt.png\" alt=\"Plot Points Using Patterns Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Plot Points Using Patterns Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/understand-decimal-point-placement-by-multiplying\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_placement_of_dec_point_1_pt.png\" alt=\"Understand Decimal point Placement by Multiplying Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Understand Decimal point Placement by Multiplying Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/understand-decimal-point-using-division\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_placement_of_dec_point_3_pt.png\" alt=\"Understand Decimal Point Using Division Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Understand Decimal Point Using Division Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/understand-decimal-point-using-multiplication\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_placement_of_dec_point_2_pt.png\" alt=\"Understand Decimal Point Using Multiplication Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Understand Decimal Point Using Multiplication Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/understand-placement-of-the-decimal-point\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_placement_of_decimal_point_4_pt.png\" alt=\"Understand Placement of the Decimal Point Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Understand Placement of the Decimal Point Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-point-of-concurrency-definition-in-geometry\">Point of concurrency Definition in Geometry<\/h2>\n\n\n\n<p><strong>In geometry, the point of concurrency refers to the single point where three or more lines, rays, or line segments intersect or come together simultaneously.<\/strong><\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/write-all-equivalent-fractions-of-marked-points\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/write-all-equivalent-fractions-of-marked-points.jpeg\" alt=\"Write All Equivalent Fractions of Marked Points Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/write-equivalent-fractions-represented-by-point\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/write-equivalent-fractions-represented-by-point.jpeg\" alt=\"Write Equivalent Fractions Represented by Point Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-concurrency-points-in-triangles\">Concurrency Points in Triangles<\/h2>\n\n\n\n<p>In a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a>, special types of lines can be drawn, such as altitudes, medians, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/angle-bisector\">angle bisectors<\/a>, or perpendicular bisectors.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"348\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-special-segments.png\" alt=\"Angle bisector, median, altitude, perpendicular bisector of a triangle\" class=\"wp-image-32401\" title=\"Angle bisector, median, altitude, perpendicular bisector of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-special-segments.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-special-segments-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Altitudes: These are the perpendicular lines drawn from the vertices of the triangle to the opposite side. A triangle has three altitudes whose point of concurrency is called orthocenter.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Medians: These line segments are drawn from the vertices of the triangle to the midpoint of the opposite side. A triangle has three medians whose point of concurrency is known as the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle\">centroid of a triangle<\/a>.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angle bisectors: These lines bisect the angles of the triangle. A triangle has three angle-bisectors (one for each angle) whose point of concurrency is incenter.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perpendicular bisectors: These are the lines that bisect the sides of the triangle at a right angle. A triangle has three perpendicular bisectors whose point of concurrency is called the circumcenter.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Only an <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/equilateral-triangle\">equilateral triangle<\/a> has the centroid, circumcenter, incenter, and orthocenter at the same point!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-equilateral-triangle.png\" alt=\"Points of concurrency in an equilateral triangle\" class=\"wp-image-32402\" title=\"Points of concurrency in an equilateral triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-equilateral-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-equilateral-triangle-300x181.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-find-points-of-concurrency\">How to Find Points Of Concurrency<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The point at which three or more lines intersect is the point of concurrency.<\/li>\n\n\n\n<li>In a triangle, for each type of line segment (altitudes, medians, angle bisectors, or perpendicular bisectors), the point of concurrency has a special name. Let\u2019s find out.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-different-points-of-concurrency-in-a-triangle\">Different Points of Concurrency in a Triangle<\/h2>\n\n\n\n<p>The different concurrent points in the triangle are referred to as different centers according to the lines meeting at that point.<\/p>\n\n\n\n<p>There are four different concurrency points in a triangle:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Centroid: The point of intersection of medians<\/li>\n\n\n\n<li>Circumcenter: The point of intersection of perpendicular bisectors<\/li>\n\n\n\n<li>Incenter: The point of intersection of angle bisectors<\/li>\n\n\n\n<li>Orthocenter: The point of intersection of altitudes<\/li>\n<\/ul>\n\n\n\n<p>Let&#8217;s discuss each point in detail.<\/p>\n\n\n\n<p><strong>Centroid: Point of Concurrency of Medians<\/strong><\/p>\n\n\n\n<p>It is a point in the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/plane-figure\">plane figure<\/a> that can be found away from the average of all the points.<\/p>\n\n\n\n<p>The centroid of a triangle is a point at which the medians of a triangle coincide. In other words, we can say that when three medians of a triangle intersect at a common point, this creates the centroid. And the point of intersection is known as the point of concurrency of medians.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"426\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-centroid.png\" alt=\"Centroid of triangle\" class=\"wp-image-32403\" title=\"Centroid of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-centroid.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-centroid-300x206.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the above figure point G is called the centroid of the triangle ABC.<\/li>\n\n\n\n<li>The centroid of a triangle intersects all three medians of a triangle in the ratio 2:1.<\/li>\n\n\n\n<li>It always lies within the triangle.<\/li>\n<\/ul>\n\n\n\n<p><strong>Circumcenter: Point of Concurrency of Perpendicular Bisectors<\/strong><\/p>\n\n\n\n<p>The point of concurrency of all the perpendicular bisectors of all sides of a triangle is known as the circumcenter.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"594\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/circumcenter.png\" alt=\"Circumcenter - the point of concurrency of perpendicular bisectors\" class=\"wp-image-32404\" title=\"Circumcenter - the point of concurrency of perpendicular bisectors\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/circumcenter.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/circumcenter-300x287.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The circumcenter is the point that is equidistant from all the vertices of the triangle.<\/li>\n\n\n\n<li>With a circumcenter as its center, a circle known as a circumcircle can be drawn by touching the vertices of the triangle.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"327\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-circumcenter.png\" alt=\"Circumcenter of triangle\" class=\"wp-image-32405\" title=\"Circumcenter of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-circumcenter.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-circumcenter-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The circumcenter of an obtuse-angled triangle is outside the triangle.<\/li>\n\n\n\n<li>For a right-angled triangle, the circumcenter lies at the hypotenuse.<\/li>\n<\/ul>\n\n\n\n<p><strong>Incenter: Point of Concurrency of Angle Bisectors<\/strong><\/p>\n\n\n\n<p>The intersection of the angle bisectors of all the interior angles of the triangle is known as the incenter.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"399\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-incenter.png\" alt=\"Incenter - the point of concurrency of the angle bisectors\" class=\"wp-image-32406\" title=\"Incenter - the point of concurrency of the angle bisectors\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-incenter.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-incenter-300x193.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>With the incenter as the center, a circle drawn by touching all sides internally is known as an incircle.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-incenter-incircle.png\" alt=\"Incenter of triangle\" class=\"wp-image-32407\" title=\"Incenter of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-incenter-incircle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-incenter-incircle-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The incenter is the point that is equidistant from the sides of the triangle.<\/li>\n\n\n\n<li>The incenter always lies within the triangle.<\/li>\n<\/ul>\n\n\n\n<p><strong>Orthocenter: Point of Concurrency of Altitudes<\/strong><\/p>\n\n\n\n<p>The point of intersection of the three altitudes is known as the orthocenter.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/QkIdqWNPt8AeCHhpiawpq_MLbYVXyDMZz_zcRDebzrw7sb3eRVtDV4ItnO6KXDE2IdB_DvLOfpLVRHZIyRcvAGzg8kDDn832TyJ-_S2wSJjg2txBVcGJSSc5gZpXTpX8NWhv7IfpDmyxb1GGwB7nvgE\" alt=\"Orthocenter of triangle\" title=\"Orthocenter of triangle\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It may lie outside of the triangle.<\/li>\n\n\n\n<li>For an obtuse-angled triangle, the orthocenter lies outside the triangle.<\/li>\n\n\n\n<li>For any right triangle, the orthocenter is at the vertex of the right angle.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/nAR7qDzIFqrtNNhstKAv84krR6idBTLRWCn_Mhm5T94fdK0GwJ8MYzozJF-eV_xV7m8WonvrtK9zdBdsIsOF_8SatG3A49okTlO97KExsEq_1coy7KdTGcKW3q2e0AjT8Q1lITrp5I9ZBqhdHfIF7bI\" alt=\"Orthocenter in a right triangle\" style=\"width:620px;height:484px\" title=\"Orthocenter in a right triangle\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-facts-about-points-of-concurrency\">Facts about Points of Concurrency<\/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-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>A triangle\u2019s centroid will always fall between the triangle\u2019s orthocenter and circumcenter.<\/li>\n\n\n\n<li>The distance from the centroid to the circumcenter is always half the distance between the centroid and orthocenter.<\/li>\n\n\n\n<li>For every right triangle, the circumcenter is always the midpoint of the hypotenuse.<\/li>\n\n\n\n<li>All four points of concurrency (centroid, circumcenter, incenter, and orthocenter) can be concurrent in itself.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have covered points of concurrency, different points of concurrency in the triangle, and important facts to know about the point of concurrency. Let us now look at some solved examples and frequently asked questions to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-point-of-concurrency\">Solved Examples on Point of Concurrency<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>In the figure given below, what is point P called?&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"180\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-in-triangles-example.png\" alt=\"Point of concurrency\" class=\"wp-image-32408\" title=\"Point of concurrency\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In the given figure, all three lines intersect at point P.&nbsp;<\/p>\n\n\n\n<p>The point P is the point of intersection of three lines.<\/p>\n\n\n\n<p>Hence, P is called the point of concurrency. Three lines are called concurrent lines.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>In the figure given below, if I represents the incenter of the triangle, then find the measure of angle \u2220ABN.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"156\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/Solved-Examples-2.png\" alt=\"Angle bisectors of triangle\" class=\"wp-image-32409\" title=\"Angle bisectors of triangle\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>We know that the incenter of a triangle is formed by the angle bisectors of a triangle.<\/p>\n\n\n\n<p>In the given figure, BN is an angle bisector of angle \u2220ABC.<\/p>\n\n\n\n<p>Hence,&nbsp; \u2220ABN=\u2220ABC2=5802=290.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>An equilateral triangle ABC as shown in the figure has each side length of 12 feet.&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>(i) Name the point P (ii) Find \u2220ABP (iii) Name the line AD, BE, and CF. (iv) Find the length of AE.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"220\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/point-of-concurrency-problem.png\" alt=\"Concurrent points of equilateral triangle\" class=\"wp-image-32410\" title=\"Concurrent points of equilateral triangle\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>(i) In the figure, point P is the point of concurrency of all three medians, altitudes, perpendicular bisectors, and angle bisectors. In an equilateral triangle, the centroid, circumcenter, orthocenter, incenter are represented by the same point.<\/p>\n\n\n\n<p>(ii) The line segment BE is the angle bisector of angle \u2220ABC.<\/p>\n\n\n\n<p>In an equilateral triangle, each interior angle measures 600.<\/p>\n\n\n\n<p>Hence,&nbsp; \u2220ABP =\u2220ABC2 = 6002 = 300.<\/p>\n\n\n\n<p>(iii) The lines AD, BE, and CF are concurrent lines. In equilateral triangles medians, altitudes, perpendicular bisectors, and angle bisectors all coincide. Hence the line AD, BE, and CF can be medians or altitudes or perpendicular bisectors, or angle bisectors.<\/p>\n\n\n\n<p>(iv) Length of AE = AC2 = 122 = 6 feet.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-point-of-concurrency\">Practice Problems on Point of Concurrency<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Point of Concurrency<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The centroid of a triangle divides the median in the ratio______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1:2<\/div><div class=\"spq_answer_block\" data-value=\"1\">2:1<\/div><div class=\"spq_answer_block\" data-value=\"2\">1:3<\/div><div class=\"spq_answer_block\" data-value=\"3\">2:3<\/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: 2:1<br\/>The centroid of a triangle divides the median in the ratio of 2:1.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The point of concurrency of the angle bisectors of all the interior angles of the triangle is known as the______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">centroid<\/div><div class=\"spq_answer_block\" data-value=\"1\">incenter<\/div><div class=\"spq_answer_block\" data-value=\"2\">circumcenter<\/div><div class=\"spq_answer_block\" data-value=\"3\">orthocenter<\/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: incenter<br\/>The point of concurrency of the angle bisectors of all the interior angles of the triangle is known as the incenter.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the name of the circle passing through all the vertices of a triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Circumcenter<\/div><div class=\"spq_answer_block\" data-value=\"1\">Incircle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Circumcircle<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these.<\/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: Circumcircle<br\/>The circle passing through all the vertices of a triangle is known as the circumcircle.<\/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\">Where does the incenter of any triangle lie?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Inside the triangle<\/div><div class=\"spq_answer_block\" data-value=\"1\">Outside the triangle<\/div><div class=\"spq_answer_block\" data-value=\"2\">At the side of the triangle.<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these.<\/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: Inside the triangle<br\/>The incenter of any triangle always lies inside the triangle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Point of concurrency of _____ is known as an orthocenter of the triangle.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">angle bisectors<\/div><div class=\"spq_answer_block\" data-value=\"1\">medians<\/div><div class=\"spq_answer_block\" data-value=\"2\">altitudes<\/div><div class=\"spq_answer_block\" data-value=\"3\">perpendicular bisectors<\/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: altitudes<br\/>The point of concurrency of altitudes is known as an orthocenter of the triangle.<\/span><\/div><\/div><\/div><\/div>  <script 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    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The circle passing through all the vertices of a triangle is known as the circumcircle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Circumcircle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The circle passing through all the vertices of a triangle is known as the circumcircle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The circle passing through all the vertices of a triangle is known as the circumcircle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Where does the incenter of any triangle lie?\",\n                    \"text\": \"Where does the incenter of any triangle lie?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The incenter of any triangle always lies inside the triangle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Outside the triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The incenter of any triangle always lies inside the triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"At the side of the triangle.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The incenter of any triangle always lies inside the triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The incenter of any triangle always lies inside the triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Inside the triangle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The incenter of any triangle always lies inside the triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The incenter of any triangle always lies inside the triangle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Point of concurrency of _____ is known as an orthocenter of the triangle.\",\n                    \"text\": \"Point of concurrency of _____ is known as an orthocenter of the triangle.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The point of concurrency of altitudes is known as an orthocenter of the triangle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"angle bisectors\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point of concurrency of altitudes is known as an orthocenter of the triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"medians\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point of concurrency of altitudes is known as an orthocenter of the triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"perpendicular bisectors\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The point of concurrency of altitudes is known as an orthocenter of the triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"altitudes\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The point of concurrency of altitudes is known as an orthocenter of the triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The point of concurrency of altitudes is known as an orthocenter of the triangle.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-about-point-of-concurrency\">Frequently Asked Questions about Point of Concurrency<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a4dab665-8cb7-4a2f-8df9-aa6db193465c\" 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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4dab665-8cb7-4a2f-8df9-aa6db193465c\"><strong>What are the different points of concurrency?<\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\">\n\n<p>The four major points of concurrency are centroid, circumcenter, incenter, and orthocenter.<\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4dab665-8cb7-4a2f-8df9-aa6db193465c\"><strong>How many points of concurrency coincide in an equilateral triangle?\u00a0<\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\">\n\n<p>In an equilateral triangle, four points of concurrency (centroid, circumcenter, incenter, and orthocenter) coincide.<\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4dab665-8cb7-4a2f-8df9-aa6db193465c\"><strong>Which triangle\u2019s circumcenter lies at the hypotenuse?<\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\">\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-triangle\">right-angled triangle<\/a>\u2019s circumcenter lies at the hypotenuse.<\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4dab665-8cb7-4a2f-8df9-aa6db193465c\"><span style=\"font-weight: 600; color: rgb(54, 54, 57);\">Which type of triangle has the orthocenter lying outside it?<\/span><\/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-a4dab665-8cb7-4a2f-8df9-aa6db193465c\">\n\n<p>An obtuse-angled triangle has an orthocenter that lies outside the triangle.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Point of Concurrency in Geometry? The point of concurrency is the point where three or more lines intersect each other or pass through. In simple words, it is the point of intersection of three or more lines.&nbsp; The word \u201cconcurrent\u201d refers to events occurring simultaneously or at the same time. In 2D &#8230; <a title=\"Point of Concurrency &#8211; Definition, Facts, Examples, Practice Problems\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/point-of-concurrency\" aria-label=\"More on Point of Concurrency &#8211; Definition, Facts, Examples, Practice Problems\">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-32398","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\/32398","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=32398"}],"version-history":[{"count":5,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32398\/revisions"}],"predecessor-version":[{"id":39940,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32398\/revisions\/39940"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}