{"id":166058,"date":"2024-04-02T15:10:51","date_gmt":"2024-04-02T09:40:51","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=166058"},"modified":"2024-04-02T15:10:53","modified_gmt":"2024-04-02T09:40:53","slug":"in-a-triangle-abc-p-and-q-are-the-mid-points-of-ab-and-bc-respectively-point-g-and-h-l-ies-on-ac-such-that-they-are","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/in-a-triangle-abc-p-and-q-are-the-mid-points-of-ab-and-bc-respectively-point-g-and-h-l-ies-on-ac-such-that-they-are\/","title":{"rendered":"In a triangle ABC, P and Q are the mid points of AB and BC respectively. Point G and H l ie\u2019s on AC such that they are"},"content":{"rendered":"\n

In a triangle ABC, P and Q are the mid points of AB and BC respectively. Point G and H l ie\u2019s on AC such that they are the mid-point of PR and QR respectively. Here R is a point outside the triangle. Then what is the Ratio of area \u2206 ABC : area \u2206 PQR?<\/p>

(a) 2 : 3<\/p>

(b) 5 : 2<\/p>

(c) 3 : 5<\/p>

(d) 2 : 1<\/b><\/p>

Sol:<\/p> <\/p>\n\n\n\n

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

\u2206 BPQ ~ \u2206 BAC<\/p>\n\n\n\n

AC = 2PQ<\/p>\n\n\n\n

AC II PQ<\/p>\n\n\n\n

BE = 2BD<\/p>\n\n\n\n

BD = DE<\/p>\n\n\n\n

\u2206 RGH ~\u2206 RPQ<\/p>\n\n\n\n

PQ = 2GH<\/p>\n\n\n\n

PQ II GH<\/p>\n\n\n\n

RY = 2RX<\/p>\n\n\n\n

\u21d2 RX = XY<\/p>\n\n\n\n

Since<\/p>\n\n\n\n

RX = XY = BD = DE<\/p>\n\n\n\n

RY = BE = h<\/p>\n\n\n\n

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

=2 : 1<\/p>\n","protected":false},"excerpt":{"rendered":"

In a triangle ABC, P and Q are the mid points of AB and BC respectively. Point G and H l ie\u2019s on AC such that they are the mid-point of PR and QR respectively. Here R is a point outside the triangle. Then what is the Ratio of area \u2206 ABC : area \u2206 […]<\/p>\n","protected":false},"author":419,"featured_media":166061,"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-166058","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\/166058","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=166058"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166058\/revisions"}],"predecessor-version":[{"id":166062,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/166058\/revisions\/166062"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/166061"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=166058"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=166058"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=166058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}