{"id":21459,"date":"2019-05-21T19:31:22","date_gmt":"2019-05-21T14:01:22","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21459"},"modified":"2022-11-16T21:22:17","modified_gmt":"2022-11-16T15:52:17","slug":"if-rectangle-abcd-is-inscribed-in-the-circle-above-what-is-the-area-of-the-circular-region-og-2020-question-96-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/if-rectangle-abcd-is-inscribed-in-the-circle-above-what-is-the-area-of-the-circular-region-og-2020-question-96-with-solution\/","title":{"rendered":"If rectangle ABCD is inscribed in the circle above, what is the area of the circular region? &#8211; OG 2020 Question #96 with Solution"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">2<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span><h2>OG 2020: Question No. 96<\/h2>\n<p><img class=\"aligncenter\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/OG_PS_96.png\"><\/p>\n<p>If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?<\/p>\n<ol>\n<li>36.00\u03c0<\/li>\n<li>42.25\u03c0<\/li>\n<li>64.00\u03c0<\/li>\n<li>84.50\u03c0<\/li>\n<li>169.00\u03c0<\/li>\n<\/ol>\n<table>\n<tbody>\n<tr>\n<td width=\"301\">Source<\/td>\n<td width=\"301\">OG 2020<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Type<\/td>\n<td width=\"301\">Problem Solving<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Topic<\/td>\n<td width=\"301\">Geometry<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Sub-Topic<\/td>\n<td width=\"301\">Circle\/Triangle<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Difficulty<\/td>\n<td width=\"301\">Medium<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Solution<\/h3>\n<h4><strong><u>Given<\/u><\/strong><\/h4>\n<p>In this question, we are given<\/p>\n<ul>\n<li>Rectangle ABCD is inscribed in the circle, as shown in the given diagram.<\/li>\n<\/ul>\n<h4><strong><u>To Find<\/u><\/strong><\/h4>\n<p>We need to determine<\/p>\n<ul>\n<li>The area of the circular region<\/li>\n<\/ul>\n<h4><strong><u>Approach &amp; Working<\/u><\/strong><\/h4>\n<p>As ABCD is a rectangle, we can say angle ADC = angle ABC = 90\u00b0<\/p>\n<ul>\n<li>Hence, we can conclude that AC is a diameter of the circle.<\/li>\n<\/ul>\n<p><em>(Note that by applying the same logic, we can say angle DAB = angle DCB = 90\u00b0, hence, DB is a diameter of the rectangle).<\/em><\/p>\n<p>Now, if we connect AC, then applying Pythagoras Theorem we can say<\/p>\n<ul>\n<li>AC<sup>2<\/sup> = AB<sup>2<\/sup> + BC<sup>2<\/sup><\/li>\n<\/ul>\n<p>Or, AC<sup>2<\/sup> = 12<sup>2<\/sup> + 5<sup>2<\/sup> = 144 + 25 = 169 = 13<sup>2<\/sup><\/p>\n<p>Or, AC = 13<\/p>\n<p>Hence, the diameter of the circle is 13 units.<\/p>\n<ul>\n<li>Radius (r) of the circle = 13 * \u00bd = 13\/2 units<\/li>\n<li>So, the area of the circle = \u03c0r<sup>2<\/sup> = \u03c0(13\/2)<sup>2<\/sup> = 169\u03c0\/4 = 42.25\u03c0<\/li>\n<\/ul>\n<p>Hence, the correct answer is option B.<\/p>\n<blockquote><p>Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don\u2019t you<a href=\"https:\/\/e-gmat.com\/ft-gmat\/?channel=blogsin_article&amp;utm_source=blogs&amp;utm_medium=in_article&amp;utm_campaign=free_trial&amp;utm_term=blogs_in_article_lekhika\" target=\"_blank\" rel=\"noopener noreferrer external\" data-wpel-link=\"external\">&nbsp;<strong>try out our FREE Trial?<\/strong><\/a><strong>&nbsp;<\/strong>We are the<strong>&nbsp;<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noopener noreferrer external\" data-wpel-link=\"external\">most reviewed online GMAT Preparation company in GMATClub<\/a><\/strong> with more than 1950 reviews as of October 2020.<\/p><\/blockquote>\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-8f3dc376-f009-46c2-80aa-263a0dd179d0\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-block-btn\">Sign up for a Free Trial<\/span>\n    <\/div><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>OG 2020: Question No. 96 If rectangle ABCD is inscribed in the circle above, what is the area of the circular region? 36.00\u03c0 42.25\u03c0 64.00\u03c0 84.50\u03c0 169.00\u03c0 Source OG 2020 Type Problem Solving Topic Geometry Sub-Topic Circle\/Triangle Difficulty Medium Solution Given In this question, we are given Rectangle ABCD is inscribed in the circle, as [&hellip;]<\/p>\n","protected":false},"author":79663,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[104,44,94,60,100],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Juhi Gupta","author_link":"https:\/\/e-gmat.com\/blogs\/author\/juhie-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If rectangle ABCD is inscribed in the circle above, what is the area of the circular region? - OG 2020 Question #96 with Solution<\/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:\/\/e-gmat.com\/blogs\/if-rectangle-abcd-is-inscribed-in-the-circle-above-what-is-the-area-of-the-circular-region-og-2020-question-96-with-solution\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If rectangle ABCD is inscribed in the circle above, what is the area of the circular region? 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