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Three concurrent circles

Source: Kürschák 2014, problem 2

October 10, 2014
geometrycircumcirclepower of a pointradical axisgeometry unsolved

Problem Statement

We are given an acute triangle ABCABC, and inside it a point PP, which is not on any of the heights AA1AA_1, BB1BB_1, CC1CC_1. The rays APAP, BPBP, CPCP intersect the circumcircle of ABCABC at points A2A_2, B2B_2, C2C_2. Prove that the circles AA1A2AA_1A_2, BB1B2BB_1B_2 and CC1C2CC_1C_2 are concurrent.
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