{"id":166668,"date":"2024-04-09T12:23:39","date_gmt":"2024-04-09T06:53:39","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=166668"},"modified":"2024-04-09T12:23:40","modified_gmt":"2024-04-09T06:53:40","slug":"in-the-given-figure-abc-is-right-angle-triangle-right-angled-at-b-a-semi-circle-is-drawn-inside-the-triangle","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/in-the-given-figure-abc-is-right-angle-triangle-right-angled-at-b-a-semi-circle-is-drawn-inside-the-triangle\/","title":{"rendered":"In the given figure ABC is right angle triangle, right angled at B. A semi -circle is drawn inside the triangle"},"content":{"rendered":"\n

In the given figure ABC is right angle triangle, right angled at B. A semi -circle is drawn inside the triangle. Find the radius of semicircle if AO = 4cm & OC = 5cm?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

(a) 15\/\u221a41<\/p>\n\n\n\n

(b)  20\/\u221a41<\/strong><\/p>\n\n\n\n

(c)  25\/\u221a41<\/p>\n\n\n\n

(d) 30\/\u221a41<\/p>\n\n\n\n

 Sol:<\/p>\n\n\n\n

\u2206ADO ~ \u2206OEC<\/p>\n\n\n\n

\u2234 in \u2206ADO, sin\u03b8 = r\/4<\/p>\n\n\n\n

and in \u2206OFC, cos\u03b8 = r\/5<\/p>\n\n\n\n

Now, sin\u00b2\u03b8 + cos\u00b2\u03b8 = 1<\/p>\n\n\n\n

=>r2\/16+r2\/25=1<\/p>\n\n\n\n

=>r2=16*25\/41<\/p>\n\n\n\n

=>r=4*5\/\u221a41=20\/\u221a41<\/p>\n","protected":false},"excerpt":{"rendered":"

In the given figure ABC is right angle triangle, right angled at B. A semi -circle is drawn inside the triangle. Find the radius of semicircle if AO = 4cm & OC = 5cm? (a) 15\/\u221a41 (b)  20\/\u221a41 (c)  25\/\u221a41 (d) 30\/\u221a41  Sol: \u2206ADO ~ \u2206OEC \u2234 in \u2206ADO, sin\u03b8 = r\/4 and in \u2206OFC, […]<\/p>\n","protected":false},"author":419,"featured_media":166670,"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-166668","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\/166668","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=166668"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166668\/revisions"}],"predecessor-version":[{"id":166671,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166668\/revisions\/166671"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/166670"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=166668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=166668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=166668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}