{"id":210,"date":"2022-04-13T08:43:28","date_gmt":"2022-04-13T08:43:28","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=210"},"modified":"2025-12-04T12:20:59","modified_gmt":"2025-12-04T12:20:59","slug":"l-9-inscribed-angles","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/l-9-inscribed-angles\/","title":{"rendered":"L.9 Inscribed angles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d\"><strong>Inscribed angles<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-869a5c0b6b78055316c8d0186252dcbd\" style=\"color:#74008b\"><strong>key notes :<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd35 <strong>What is an Inscribed Angle?<\/strong><\/h3>\n\n\n\n<p>An <strong>inscribed angle<\/strong> is an angle whose <strong>vertex lies on the circle<\/strong>, and its <strong>sides (arms)<\/strong> touch the circle.<br>\ud83d\udc49 It \u201csits\u201d on the circle\u2019s boundary.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd34 <strong>Intercepted Arc \ud83c\udfaf<\/strong><\/h3>\n\n\n\n<p>The <strong>intercepted arc<\/strong> is the part of the circle <strong>cut off<\/strong> or <strong>covered<\/strong> by the inscribed angle.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe2 <strong>Inscribed Angle Theorem \ud83d\udca1<\/strong><\/h3>\n\n\n\n<p>The measure of an <strong>inscribed angle = \u00bd \u00d7 measure of the intercepted arc<\/strong>.<br>\ud83d\udccc If the arc is 80\u00b0, the inscribed angle is <strong>40\u00b0<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe3 <strong>Angles on the Same Arc Are Equal \u2696\ufe0f<\/strong><\/h3>\n\n\n\n<p>If two inscribed angles intercept the <strong>same arc<\/strong>, they have the <strong>same measure<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe0 <strong>Angle in a Semicircle = 90\u00b0 \u2b55<\/strong><\/h3>\n\n\n\n<p>If the endpoints of an inscribed angle lie on the <strong>diameter<\/strong>, the angle is a <strong>right angle (90\u00b0)<\/strong>.<br>\ud83d\udc49 Also called <strong>Thales&#8217; Theorem<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe1 <strong>Inscribed vs. Central Angles \ud83c\udd9a<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Central angle<\/strong> = vertex at the <strong>center<\/strong>; equals the <strong>arc<\/strong>.<\/li>\n\n\n\n<li><strong>Inscribed angle<\/strong> = vertex on the <strong>circle<\/strong>; equals <strong>half of the arc<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccc Example: If a central angle is 100\u00b0, the inscribed angle on the same arc is <strong>50\u00b0<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd35 <strong>Useful for Solving Problems \u270f\ufe0f<\/strong><\/h3>\n\n\n\n<p>You can use inscribed angles to find:<br>\u2714 Missing angle measures<br>\u2714 Arc lengths<br>\u2714 Right triangles inside circles<br>\u2714 Relations with central angles<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-d99337844886c8fe971516063c7555f8\" style=\"background-color:#d1efd5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color has-large-font-size wp-elements-cd50955d4c394423114939bc224f4b8c\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-2849a6155e82a91cfd16cc1f5a00ec4d\" style=\"color:#b00012\"><strong>What&nbsp;is \u2220HGI?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-38.png\" alt=\"\" class=\"wp-image-11864\" style=\"width:292px;height:auto\"\/><\/figure><\/div>\n\n\n<p>\u2220HGI= _____\u2218<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;diagram:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-23.png\" alt=\"\" class=\"wp-image-11871\" style=\"width:284px;height:auto\"\/><\/figure><\/div>\n\n\n<p>\u2220HGI is an inscribed angle that intercepts the same arc as the central angle \u2220J, so use the Inscribed Angle Theorem.<\/p>\n\n\n\n<h1 class=\"wp-block-heading has-large-font-size\">\u2220HGI =1\/2 . \u2220j<\/h1>\n\n\n\n<p>         =1\/2 (122\u00b0) plug \u2220J=122\u00b0<\/p>\n\n\n\n<p>         =61\u00b0<\/p>\n\n\n\n<p>\u2220HGI is 61\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-3e7c334c74a1c6db0e0c3ead72a76117\" style=\"background-color:#f6f6b6\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color has-large-font-size wp-elements-8b113a3ab508ac39c1ffa28557a87f58\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8fa88ccf51fd1fc3517b82fd2401c8d1\" style=\"color:#b00012\"><strong>What is \u2220F?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-9.png\" alt=\"\" class=\"wp-image-11884\" style=\"width:259px;height:auto\"\/><\/figure><\/div>\n\n\n<p>\u2220F= ________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;diagram:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-24.png\" alt=\"\" class=\"wp-image-11892\" style=\"width:264px;height:auto\"\/><\/figure><\/div>\n\n\n<p>\u2220GHI is an inscribed angle that intercepts the same arc as the central angle \u2220F, so use the Inscribed Angle Theorem.<\/p>\n\n\n\n<p>\u2220F= 2 . \u2220GHI     Inscribed Angle Theorem<\/p>\n\n\n\n<p>= 2 .(47\u00b0)       Plug in   \u2220GHI=47\u00b0<\/p>\n\n\n\n<p>= 94\u00b0 Multiply<\/p>\n\n\n\n<p>\u2220F is 94\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d1e6f7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-736844ee4de2e05ecafa37fdbef647f6\" style=\"color:#b00012\"><strong>What is \u2220J?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-41.png\" alt=\"\" class=\"wp-image-11895\" style=\"width:326px;height:auto\"\/><\/figure><\/div>\n\n\n<p>\u2220J=______ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look at the diagram:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-28.png\" alt=\"\" class=\"wp-image-11896\" style=\"width:297px;height:auto\"\/><\/figure><\/div>\n\n\n<p>\u2220GHI is an inscribed angle that intercepts the same arc as the central angle \u2220J, so use the Inscribed Angle Theorem.<br>\u2220J = 2 . \u2220GHI    Inscribed Angle Theorem<br>= 2 . (65\u00b0)       Plug in \u2220GHI=65\u00b0<br>= 130\u00b0         Multiply<br>\u2220J is 130\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/88999\/962\/106\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-75.png\" alt=\"\" class=\"wp-image-7913\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-75.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-75-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-75-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/88999\/383\/348\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84.png\" alt=\"\" class=\"wp-image-7914\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-84-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Inscribed angles key notes : \ud83d\udd35 What is an Inscribed Angle? An inscribed angle is an angle whose vertex lies on the circle, and its sides (arms) touch the circle.\ud83d\udc49 It \u201csits\u201d on the circle\u2019s boundary. \ud83d\udd34 Intercepted Arc \ud83c\udfaf The intercepted arc is the part of the circle cut off or covered by the<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/l-9-inscribed-angles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.9 Inscribed angles&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-210","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=210"}],"version-history":[{"count":18,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/210\/revisions"}],"predecessor-version":[{"id":18296,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/210\/revisions\/18296"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}