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2001 Spanish Mathematical Olympiad, Problem 2

Source: Spanish Mathematical Olympiad 2001

June 5, 2017
geometrysimilar triangles

Problem Statement

Let PP be a point on the interior of triangle ABCABC, such that the triangle ABPABP satisfies AP=BPAP = BP. On each of the other sides of ABCABC, build triangles BQCBQC and CRACRA exteriorly, both similar to triangle ABPABP satisfying: BQ=QCBQ = QC and CR=RA.CR = RA. Prove that the point P,Q,C,P,Q,C, and RR are collinear or are the vertices of a parallelogram.
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