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Concurrency on coplanar triangles

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January 3, 2011
Eulerratiosymmetrygeometry

Problem Statement

Let ABCABC and A′B′C′A'B'C' be any two coplanar triangles. Let LL be a point such that AL∣∣BC,A′L∣∣B′C′AL || BC, A'L || B'C' , and M,NM,N similarly defined. The line BCBC meets B′C′B'C' at PP, and similarly defined are QQ and RR. Prove that PL,QM,RNPL, QM, RN are concurrent.
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