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Centroamerican Olympiad 2010, problem 2

Source:

May 30, 2010
geometrycircumcircleprojective geometrygeometry proposed

Problem Statement

Let ABCABC be a triangle and LL, MM, NN be the midpoints of BCBC, CACA and ABAB, respectively. The tangent to the circumcircle of ABCABC at AA intersects LMLM and LNLN at PP and QQ, respectively. Show that CPCP is parallel to BQBQ.
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