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trinagle inscirbed in triangle, equal ratio

Source: Polish MO second round 1951 p2

August 28, 2024
geometryareasinscribedratio

Problem Statement

In the triangle ABC ABC on the sides BC BC , CA CA , AB AB , the points D D , E E , F F are chosen respectively in such a way that BD ⁣:DC=CE ⁣:EA=AF ⁣:FB=k, BD \colon DC = CE \colon EA = AF \colon FB = k, where kk is a given positive number. Given the area S S of the triangle ABC ABC , calculate the area of the triangle DEF DEF
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