{"id":11450,"date":"2022-07-11T16:39:02","date_gmt":"2022-07-11T11:09:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11450"},"modified":"2022-07-11T16:39:07","modified_gmt":"2022-07-11T11:09:07","slug":"pqr-is-a-triangle-right-angled-at-p-and-m-is-a-point-on-qr-such-that-pm-perp-qr-show-that-pm2-qm-mr","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/pqr-is-a-triangle-right-angled-at-p-and-m-is-a-point-on-qr-such-that-pm-perp-qr-show-that-pm2-qm-mr\/","title":{"rendered":"PQR is a triangle right angled at P and M is a point on QR such that PM \\(\\perp\\) QR. Show that \\({PM}^2\\) = QM.MR."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Since, PM \\(\\perp\\) QR, therefore,<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11458 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-2.jpeg?resize=171%2C162&#038;ssl=1\" alt=\"triangle\" width=\"171\" height=\"162\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-2.jpeg?resize=300%2C285&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-2.jpeg?resize=1024%2C973&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-2.jpeg?resize=768%2C730&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-2.jpeg?resize=1536%2C1459&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-5-2.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 171px) 100vw, 171px\" data-recalc-dims=\"1\" \/><\/p>\n<p>\\(\\triangle\\) PQM ~ \\(\\triangle\\) RPM<\/p>\n<p>\\(\\implies\\)\u00a0 \\(PM\\over QM\\) = \\(MR\\over PM\\)<\/p>\n<p>So, <strong>\\({PM}^2\\) = QM.MR<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Since, PM \\(\\perp\\) QR, therefore, \\(\\triangle\\) PQM ~ \\(\\triangle\\) RPM \\(\\implies\\)\u00a0 \\(PM\\over QM\\) = \\(MR\\over PM\\) So, \\({PM}^2\\) = QM.MR.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,912],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>PQR is a triangle right angled at P and M is a point on QR such that PM \\(\\perp\\) QR. Show that \\({PM}^2\\) = QM.MR. - Mathemerize<\/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:\/\/mathemerize.com\/pqr-is-a-triangle-right-angled-at-p-and-m-is-a-point-on-qr-such-that-pm-perp-qr-show-that-pm2-qm-mr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"PQR is a triangle right angled at P and M is a point on QR such that PM \\(\\perp\\) QR. 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