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Prove AP/AQ = 3/2

Source: Argentina TST 2009

May 15, 2009
geometrycircumcirclegeometric transformationhomothetyreflectionpower of a pointradical axis

Problem Statement

Let ABC ABC be a triangle, B1 B_1 the midpoint of side AB AB and C1 C_1 the midpoint of side AC AC. Let P P be the point of intersection (≠A \neq A) of the circumcircles of triangles ABC1 ABC_1 and AB1C AB_1C. Let Q Q be the point of intersection (≠A \neq A) of the line AP AP and the circumcircle of triangle AB1C1 AB_1C_1. Prove that \frac{AP}{AQ} \equal{} \frac{3}{2}.
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