{"id":9111,"date":"2020-12-04T08:00:06","date_gmt":"2020-12-04T02:30:06","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=9111"},"modified":"2020-12-04T16:15:31","modified_gmt":"2020-12-04T10:45:31","slug":"arcs-in-circles","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/arcs-in-circles\/","title":{"rendered":"Arcs in Circles"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\">Arcs in Circles<\/span><\/h2>\n<p>An <strong>arc<\/strong> is part of a circle&#8217;s circumference.<\/p>\n<p><strong>Definition:<\/strong><br \/>\nIn a circle, the <strong>degree measure of an arc<\/strong> is equal to the measure of the central angle that intercepts the arc.<br \/>\n<strong><img loading=\"lazy\" class=\"alignnone size-full wp-image-124122 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-1.jpg\" alt=\"Arcs in Circles 1\" width=\"103\" height=\"111\" \/>Definition:<\/strong><br \/>\nIn a circle, the <strong>length of an arc<\/strong> is a portion of the circumference.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-124123 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-2.jpg\" alt=\"Arcs in Circles 2\" width=\"223\" height=\"50\" \/><br \/>\nRemembering that the arc measure is the measure of the central angle, a definition can be formed as:<br \/>\n<strong><img loading=\"lazy\" class=\"alignnone size-full wp-image-124124 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-3.jpg\" alt=\"Arcs in Circles 3\" width=\"314\" height=\"48\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-3.jpg 314w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-3-300x46.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/>Example:<\/strong><br \/>\nIn circle O, the radius is 8, and the measure of minor arc is 110 degrees. Find the length of minor arc to the nearest integer.<br \/>\n<strong><img loading=\"lazy\" class=\"alignnone size-full wp-image-124126 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-4.jpg\" alt=\"Arcs in Circles 4\" width=\"154\" height=\"145\" \/>Solution:<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-124127 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-5.jpg\" alt=\"Arcs in Circles 5\" width=\"376\" height=\"115\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-5.jpg 376w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-5-300x92.jpg 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/>Understanding how an arc is measured makes the next theorems common sense.<br \/>\n<strong>Theorem:<\/strong><br \/>\nIn the same circle, or congruent circles, congruent central angles have congruent arcs.<br \/>\n<strong><img loading=\"lazy\" class=\"alignnone size-full wp-image-124128 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-6.jpg\" alt=\"Arcs in Circles 6\" width=\"134\" height=\"141\" \/>Theorem: (converse)<\/strong><br \/>\nIn the same circle, or congruent circles, congruent arcs have congruent central angles.<br \/>\nRemember: In the same circle, or congruent circles, congruent arcs have congruent chords. Knowing this theorem makes the next theorems seem straight forward.<\/p>\n<p><strong>Theorem:<\/strong><br \/>\nIn the same circle, or congruent circles, congruent central angles have congruent chords.<br \/>\n<strong><img loading=\"lazy\" class=\"alignnone size-full wp-image-124129 aligncenter\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-7.jpg\" alt=\"Arcs in Circles 7\" width=\"133\" height=\"132\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-7.jpg 133w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2016\/12\/Arcs-in-Circles-7-100x100.jpg 100w\" sizes=\"(max-width: 133px) 100vw, 133px\" \/>Theorem: (converse)<\/strong><br \/>\nIn the same circle, or congruent circles, congruent chords have congruent central angles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Arcs in Circles An arc is part of a circle&#8217;s circumference. Definition: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. Definition: In a circle, the length of an arc is a portion of the circumference. Remembering that the arc measure is &#8230; <a title=\"Arcs in Circles\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/arcs-in-circles\/\" aria-label=\"More on Arcs in Circles\">Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3340],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Arcs in Circles - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/arcs-in-circles\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Arcs in Circles\" \/>\n<meta property=\"og:description\" content=\"Arcs in Circles An arc is part of a circle&#8217;s circumference. 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