{"id":1463,"date":"2022-04-19T10:33:34","date_gmt":"2022-04-19T10:33:34","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1463"},"modified":"2024-02-20T18:01:28","modified_gmt":"2024-02-20T18:01:28","slug":"arc-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc","title":{"rendered":"Arc &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-2ed48aa9-5121-4109-99e6-61e333a13e30\" 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\/geometry\/arc#0-what-is-arc-in-math->What is Arc in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc#1-how-to-make-an-arc>How to Make an Arc<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc#2-types-of-arcs->Types of Arcs<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc#5-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc#6-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc#7-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-arc-in-math-\"><strong>What is Arc in Math?<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference. So, the arc is the distance between any two points traced along its circumference.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us understand this with the help of an example:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/an-arc.png\" alt=\"An arc\" class=\"wp-image-40634\" title=\"An arc\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/an-arc.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/an-arc-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In this figure, the distance between points A and B is an arc traced along the circumference of the circle. You can call it arc AB. An arc is denoted by the symbol \u201c\u2322\u201d. So, the arc AB can be written as $\\widehat{AB}$. You can also write it as $\\widehat{BA}$. The order of the points does not matter.<\/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\/classify-shapes-according-to-their-hierarchy\" 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\/geometry_whr_does_shape_belong_pt.png\" alt=\"Classify Shapes According to their Hierarchy 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\">Classify Shapes According to their Hierarchy 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 eplus-wrapper\" id=\"1-how-to-make-an-arc\">How to Make an Arc<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To make an arc, you either need a chord or a central angle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A chord is a line segment that joins any two points on a circle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"309\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-chord.png\" alt=\"A chord\" class=\"wp-image-40635\" title=\"A chord\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-chord.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-chord-300x150.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A central angle is an angle between any two radii of the circle. For instance, the central angle in the diagram between the radii QA and QB, as shown below, is 60\u00b0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-central-angle-of-60-degrees.png\" alt=\"A central angle of 60 degrees\" class=\"wp-image-40636\" title=\"A central angle of 60 degrees\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-central-angle-of-60-degrees.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-central-angle-of-60-degrees-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-types-of-arcs-\"><strong>Types of Arcs<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper\">You must have noticed that an arc divides a circle into two parts.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">One has a shorter distance between the two endpoints (minor arc), while the other has a longer distance (major arc).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"304\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/minor-arc-and-major-arc.png\" alt=\"Minor arc and major arc\" class=\"wp-image-40638\" title=\"Minor arc and major arc\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/minor-arc-and-major-arc.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/minor-arc-and-major-arc-300x147.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Unless specified, an arc will always be considered a minor arc. To specify the major arc, you can take a third point on the arc of the circle and use three letters in the name.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"373\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/central-angle-minor-arc-and-major-arc.png\" alt=\"Central angle, minor arc, and major arc\" class=\"wp-image-40637\" title=\"Central angle, minor arc, and major arc\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/central-angle-minor-arc-and-major-arc.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/central-angle-minor-arc-and-major-arc-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the diagram above, $\\widehat{AB}$ is the minor arc, and $\\widehat{ADB}$ is the major arc.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-semicircle-arc\">Semicircle Arc<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A semicircle is an arc that has its endpoints on the diameter of a circle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/semicircular-arcs.png\" alt=\"Semicircular arcs\" class=\"wp-image-40639\" title=\"Semicircular arcs\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/semicircular-arcs.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/semicircular-arcs-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-the-arc-length\">How to Find the Arc Length?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">You can calculate the length of an arc by using the formula given below.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Arc length of a circle = $\\frac{y}{360}$ &nbsp;\u2715 $2 \u03c0 r$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where r = the radius of the circle<\/p>\n\n\n\n<p class=\"eplus-wrapper\">y = the angle (in degrees) subtended by an arc at the center of the circle<\/p>\n\n\n\n<p class=\"eplus-wrapper\">360 = the angle of one complete rotation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The value of $\u03c0$ (pi) = 3.14<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Calculate the length of an arc that subtends an angle of 60 degrees at the center of a circle with a radius of 5 cm.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: We know the arc length formula is $\\frac{y}{360} \u2715 $2 \u03c0 r$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">y = 60 and r = 5<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting these values in the example, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Arc length = $\\frac{60}{360}$ \u2715 2 \u2715 3.14 \u2715 5 = 5.23 cm<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Calculate the length of the arc that subtends an angle of 40 degrees at the center of a circle with a radius of 6 cm.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We know the arc length formula is $\\frac{y}{360}$ \u2715 $2 \u03c0 r$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">y = 40 and r = 6<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting these values in the example, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Arc length = $\\frac{40}{360}$ \u2715 2 \u2715 3.14 \u2715 6 = 4.186 cm<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: Identify the major arc in this circle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"293\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-circle-with-adc-as-major-arc-Solution.png\" alt=\"A circle with ADC as major arcSolution:\" class=\"wp-image-40640\" title=\"A circle with ADC as major arcSolution:\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-circle-with-adc-as-major-arc-Solution.png 293w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-circle-with-adc-as-major-arc-Solution-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-circle-with-adc-as-major-arc-Solution-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/a-circle-with-adc-as-major-arc-Solution-120x120.png 120w\" sizes=\"auto, (max-width: 293px) 100vw, 293px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We know that a major arc is a long distance between two endpoints. So here, $\\widehat{ADC}$ is the major arc, and $\\widehat{ABC}$ is the minor arc.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Arc - 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\">Calculate the length of the arc that subtends an angle of 120 degrees at the center of a circle with a radius of 10 cm.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">20.93 cm<\/div><div class=\"spq_answer_block\" data-value=\"1\">10.93 cm<\/div><div class=\"spq_answer_block\" data-value=\"2\">14.56 cm<\/div><div class=\"spq_answer_block\" data-value=\"3\">30.46 cm<\/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: 20.93 cm<br\/>Arc length = $\\frac{y}{360}$ \u2715 $2 \u03c0 r$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $\\frac{40}{360}$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Identify the minor arc in the figure given below.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\widehat{AB}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\widehat{BD}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\widehat{DA}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\widehat{ADB}$<\/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: $\\widehat{AB}$<br\/>$\\widehat{AB}$ is the minor arc in this diagram.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Practice-Problems-2-5.png\"><\/div><\/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\">An arc on the circle is drawn so that it covers a quarter of the circumference. What will be the value of the central angle in this case?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">90\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">60\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">45\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">30\u00b0<\/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: 90\u00b0<br\/>For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Practice-Problems-3-4.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of these central angles will create the greatest arc?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">81\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">76\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">45\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">99\u00b0<\/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: 99\u00b0<br\/>The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.<\/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\": \"Arc - Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Arc\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Calculate the length of the arc that subtends an angle of 120 degrees at the center of a circle with a radius of 10 cm.\",\n                    \"text\": \"Calculate the length of the arc that subtends an angle of 120 degrees at the center of a circle with a radius of 10 cm.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Arc length = $$\\\\frac{y}{360}$$ \u2715 $$2 \u03c0 r$$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $$\\\\frac{40}{360}$$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10.93 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Arc length = $$\\\\frac{y}{360}$$ \u2715 $$2 \u03c0 r$$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $$\\\\frac{40}{360}$$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14.56 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Arc length = $$\\\\frac{y}{360}$$ \u2715 $$2 \u03c0 r$$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $$\\\\frac{40}{360}$$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30.46 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Arc length = $$\\\\frac{y}{360}$$ \u2715 $$2 \u03c0 r$$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $$\\\\frac{40}{360}$$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"20.93 cm\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Arc length = $$\\\\frac{y}{360}$$ \u2715 $$2 \u03c0 r$$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $$\\\\frac{40}{360}$$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Arc length = $$\\\\frac{y}{360}$$ \u2715 $$2 \u03c0 r$$<br>\r\nSubstituting y = 120 and r = 10 cm, we get<br>\r\nArc length = $$\\\\frac{40}{360}$$ \u2715 2 \u2715 3.14 \u2715 10 = 20.93 cm\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the minor arc in the figure given below.\",\n                    \"text\": \"Identify the minor arc in the figure given below.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\widehat{AB}$$ is the minor arc in this diagram.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\widehat{BD}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\widehat{AB}$$ is the minor arc in this diagram.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\widehat{DA}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\widehat{AB}$$ is the minor arc in this diagram.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\widehat{ADB}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\widehat{AB}$$ is the minor arc in this diagram.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\widehat{AB}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\widehat{AB}$$ is the minor arc in this diagram. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Practice-Problems-2-5.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\widehat{AB}$$ is the minor arc in this diagram. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Practice-Problems-2-5.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"An arc on the circle is drawn so that it covers a quarter of the circumference. What will be the value of the central angle in this case?\",\n                    \"text\": \"An arc on the circle is drawn so that it covers a quarter of the circumference. What will be the value of the central angle in this case?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"90\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Practice-Problems-3-4.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"For an arc that spans a quarter of the circle, the radii drawn from its endpoints will be perpendicular to each other. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Practice-Problems-3-4.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of these central angles will create the greatest arc?\",\n                    \"text\": \"Which of these central angles will create the greatest arc?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"81\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"76\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"99\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The central angle is formed by joining the endpoints of the arc with the center of the circle. Hence, the greater the central angle, the greater will be the length of the arc formed.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\" 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-0-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\"><strong>What is a semicircle arc?<\/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-0-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\">\n\n<p>A semicircle is an arc that has its endpoints on the diameter of the circle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"391\" height=\"211\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Frequently-Asked-Questions-1.png\" alt=\"Two Semicircle arcs\" class=\"wp-image-7501\" title=\"Two Semicircle arcs\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Frequently-Asked-Questions-1.png 391w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/Frequently-Asked-Questions-1-300x162.png 300w\" sizes=\"auto, (max-width: 391px) 100vw, 391px\" \/><\/figure>\n\n\n\n<p>Here, both $\\widehat{AB}$ and $\\widehat{ACB}$ are semicircle arcs.<\/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-1-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\"><strong>What is the central angle of an arc?<\/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-1-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\">\n\n<p>A central angle is an angle that an arc subtends at the center.<\/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-2-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\"><strong>Can an arc be a straight line?<\/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-2-5d98f9f2-1a5a-4b6f-b6c6-da2f8fe643f7\">\n\n<p>No. An arc is always an open curve.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What is Arc in Math? In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference. So, the arc &#8230; <a title=\"Arc &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/arc\" aria-label=\"More on Arc &#8211; 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-1463","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\/1463","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=1463"}],"version-history":[{"count":27,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1463\/revisions"}],"predecessor-version":[{"id":40641,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1463\/revisions\/40641"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1463"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1463"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}