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Construct a triangle

Source: Middle European Mathematical Olympiad 2013 T-5

May 17, 2014
trigonometrygeometry proposedgeometrybir tinga qimmat masala

Problem Statement

Let ABCABC be and acute triangle. Construct a triangle PQRPQR such that AB=2PQ AB = 2PQ , BC=2QR BC = 2QR , CA=2RP CA = 2 RP , and the lines PQ,QR, PQ, QR, and RPRP pass through the points A,B, A, B , and C C , respectively. (All six points A,B,C,P,Q, A, B, C, P, Q, and R R are distinct.)
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