{"id":134819,"date":"2023-03-21T16:36:29","date_gmt":"2023-03-21T11:06:29","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=134819"},"modified":"2023-03-21T16:36:29","modified_gmt":"2023-03-21T11:06:29","slug":"two-concentric-circles-with-centre-o-are-of-radii-3-cm-and-5-cm-find-the-length-of-chord-ab-of-the-larger-circle-which-touches-the-smaller-circle-at-p","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/two-concentric-circles-with-centre-o-are-of-radii-3-cm-and-5-cm-find-the-length-of-chord-ab-of-the-larger-circle-which-touches-the-smaller-circle-at-p","title":{"rendered":"Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P."},"content":{"rendered":"<h2>Question :Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P.<\/h2>\n<h3>The correct answer :Let Q be the center of the smaller circle, and let R be the point where the chord AB intersects the radius PO extended through O.<\/h3>\n<h3>Since PO is perpendicular to AB, we have two right triangles, OPR and OQR. Let x be the length of RP, and let y be the length of RQ. Then, we have:<\/h3>\n<h3>x\u00b2 + 3\u00b2 = 5\u00b2 (by the Pythagorean theorem in triangle OPR) y\u00b2 + 3\u00b2 = 4\u00b2 (by the Pythagorean theorem in triangle OQR)<\/h3>\n<h3>Simplifying, we get:<\/h3>\n<h3>x\u00b2 = 16 y\u00b2 = 7<\/h3>\n<h3>Taking the square root of both sides, we get:<\/h3>\n<h3>x = 4 y \u2248 2.646<\/h3>\n<h3>Now, we can use the fact that OP = OQ = 3 cm to find the length of PB. Since OB is a radius of the larger circle, we have OB = 5 cm.<\/h3>\n<h3>Therefore, PB = OB &#8211; OP = 5 &#8211; 3 = 2 cm.<\/h3>\n<h3>Finally, we can use the fact that RP = 4 cm and PB = 2 cm to find the length of chord AB:<\/h3>\n<h3>AB = RP + PB = 4 + 2 = 6 cm<\/h3>\n<h3>Therefore, the length of chord AB of the larger circle which touches the smaller circle at P is 6 cm.<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Question :Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P. The correct answer :Let Q be the center of the smaller circle, and let R be the point where the chord AB intersects [&hellip;]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-134819","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134819","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=134819"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134819\/revisions"}],"predecessor-version":[{"id":134820,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134819\/revisions\/134820"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=134819"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=134819"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=134819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}