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If ABPE is cyclic, DP parallel to AB

Source: Argentina IMO TST Problem 5

August 27, 2009
geometrycyclic quadrilateralpower of a pointradical axisgeometry unsolvedHarmonic Quadrilateral

Problem Statement

Let ABC ABC be a triangle, D D, E E and F F the points of tangency of the incircle with sides BC BC, CA CA, AB AB respectively. Let P P be the second point of intersection of CF CF and the incircle. If ABPE ABPE is a cyclic quadrilateral prove that DP DP is parellel to AB AB
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