Let ABC be a triangle and let ω be its incircle. Denote by D1 and E1 the points where ω is tangent to sides BC and AC, respectively. Denote by D2 and E2 the points on sides BC and AC, respectively, such that CD2=BD1 and CE2=AE1, and denote by P the point of intersection of segments AD2 and BE2. Circle ω intersects segment AD2 at two points, the closer of which to the vertex A is denoted by Q. Prove that AQ=D2P. USA(J)MOUSAMOgeometrygeometric transformationhomothetyparallelogramgeometry solved