{"id":265967,"date":"2025-07-22T14:48:43","date_gmt":"2025-07-22T14:48:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265967"},"modified":"2025-07-22T14:49:39","modified_gmt":"2025-07-22T14:49:39","slug":"true-or-false-11","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/true-or-false-11\/","title":{"rendered":"&#8216;True or false"},"content":{"rendered":"\n<p>&#8216;True or false? A circle could be circumscribed about the quadrilateral below. Question 5 of 10 2 Points True or False? A circle could be circumscribed about the quadrilateral below: True False&#8217;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-638.png\" alt=\"\" class=\"wp-image-265971\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The statement is <strong>True<\/strong>, provided the quadrilateral is a <strong>cyclic quadrilateral<\/strong>.<\/p>\n\n\n\n<p>A cyclic quadrilateral is one in which all four vertices lie on a single circle. This means that the quadrilateral can be circumscribed about a circle. The defining property of a cyclic quadrilateral is that the sum of the opposite angles is always 180\u00b0.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Key Conditions for a Circle to Be Circumscribed Around a Quadrilateral:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Opposite Angles Add Up to 180\u00b0<\/strong>: In any cyclic quadrilateral, the sum of opposite angles is 180\u00b0. This is a fundamental theorem of cyclic quadrilaterals, often referred to as the <strong>cyclic quadrilateral angle theorem<\/strong>.<\/li>\n\n\n\n<li><strong>Circumscribed Circle<\/strong>: A circle that passes through all four vertices of the quadrilateral is called the circumscribed circle. This circle&#8217;s center is equidistant from the vertices of the quadrilateral.<\/li>\n\n\n\n<li><strong>Ptolemy\u2019s Theorem<\/strong>: For a quadrilateral to be cyclic, Ptolemy\u2019s Theorem must hold, which states that the product of the diagonals of the quadrilateral is equal to the sum of the products of opposite sides.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Example of Cyclic Quadrilateral:<\/h3>\n\n\n\n<p>A square or rectangle is an example of a cyclic quadrilateral, as all of their vertices lie on the circumference of a circle. Other quadrilaterals, such as trapezoids or general irregular quadrilaterals, may or may not be cyclic.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>If the quadrilateral in question satisfies the properties mentioned above, such as having opposite angles summing to 180\u00b0 or fulfilling Ptolemy&#8217;s Theorem, then it is cyclic, and a circle can be circumscribed about it. If not, it is non-cyclic, and no circle can be drawn around it.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1517.jpeg\" alt=\"\" class=\"wp-image-265968\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>&#8216;True or false? A circle could be circumscribed about the quadrilateral below. Question 5 of 10 2 Points True or False? A circle could be circumscribed about the quadrilateral below: True False&#8217; The Correct Answer and Explanation is: The statement is True, provided the quadrilateral is a cyclic quadrilateral. A cyclic quadrilateral is one in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-265967","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265967","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=265967"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265967\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265967"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265967"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}