{"id":167052,"date":"2024-04-24T13:46:30","date_gmt":"2024-04-24T08:16:30","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=167052"},"modified":"2024-04-24T13:46:31","modified_gmt":"2024-04-24T08:16:31","slug":"in-a-circle-with-center-o-an-arc-abc-subtends-an-angle-of-132-degree-at-the-center-of-the-circle-chord-ab-is-produced-to","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/in-a-circle-with-center-o-an-arc-abc-subtends-an-angle-of-132-degree-at-the-center-of-the-circle-chord-ab-is-produced-to\/","title":{"rendered":"In a circle with center O, an arc ABC subtends an angle of 132 degree at the center of the circle. Chord AB is produced to"},"content":{"rendered":"\n<p>In a circle with center O, an arc ABC subtends an angle of 132 degree at the center of the circle. Chord AB is produced to point P, find angle CBP<\/p>\n\n\n\n<p>(a) 48<\/p>\n\n\n\n<p>(b) 68<\/p>\n\n\n\n<p><strong>(c) 66<\/strong><\/p>\n\n\n\n<p>(d) 76<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>As we know<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"733\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-1024x733.png\" alt=\"\" class=\"wp-image-167058\" style=\"width:166px;height:auto\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-1024x733.png 1024w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-300x215.png 300w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-768x550.png 768w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-1536x1100.png 1536w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-2048x1467.png 2048w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-209x150.png 209w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-100x72.png 100w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-489x350.png 489w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277-788x564.png 788w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2024\/04\/image-277.png 222w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>The&nbsp;angle&nbsp;subtended by an arc at the&nbsp;centre&nbsp;of a&nbsp;circle&nbsp;is double the size of the&nbsp;angle&nbsp;subtended by the same arc at the&nbsp;circle circumference&nbsp;<\/p>\n\n\n\n<p>Take any point Q on the circumference and join AQ and QC.&nbsp;<\/p>\n\n\n\n<p>\u2234 \u2220AOC = 2 \u00d7 \u2220AQC&nbsp;<\/p>\n\n\n\n<p>\u21d2 \u2220AQC = 1\/2 \u00d7 \u2220AOC = 1\/2 \u00d7 132\u00b0 = 66\u00b0&nbsp;<\/p>\n\n\n\n<p>Now, \u2220CBP = \u2220AQC&nbsp;&nbsp; [Exterior angle of cyclic quadrilateral]&nbsp;<\/p>\n\n\n\n<p>\u21d2 \u2220CBP = 66\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a circle with center O, an arc ABC subtends an angle of 132 degree at the center of the circle. Chord AB is produced to point P, find angle CBP (a) 48 (b) 68 (c) 66 (d) 76 Sol: As we know The&nbsp;angle&nbsp;subtended by an arc at the&nbsp;centre&nbsp;of a&nbsp;circle&nbsp;is double the size of the&nbsp;angle&nbsp;subtended [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":167065,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5138],"tags":[5139],"class_list":["post-167052","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/167052","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=167052"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/167052\/revisions"}],"predecessor-version":[{"id":167066,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/167052\/revisions\/167066"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/167065"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=167052"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=167052"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=167052"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}