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USAMO 2001 Problem 2

Source:

September 30, 2005
USA(J)MOUSAMOgeometrygeometric transformationhomothetyparallelogramgeometry solved

Problem Statement

Let ABCABC be a triangle and let ω\omega be its incircle. Denote by D1D_1 and E1E_1 the points where ω\omega is tangent to sides BCBC and ACAC, respectively. Denote by D2D_2 and E2E_2 the points on sides BCBC and ACAC, respectively, such that CD2=BD1CD_2=BD_1 and CE2=AE1CE_2=AE_1, and denote by PP the point of intersection of segments AD2AD_2 and BE2BE_2. Circle ω\omega intersects segment AD2AD_2 at two points, the closer of which to the vertex AA is denoted by QQ. Prove that AQ=D2PAQ=D_2P.
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