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Point P in interior of ABCD

Source: 2014 CMO #4

May 11, 2014
geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

The quadrilateral ABCDABCD is inscribed in a circle. The point PP lies in the interior of ABCDABCD, and ∠PAB=∠PBC=∠PCD=∠PDA\angle P AB = \angle P BC = \angle P CD = \angle P DA. The lines ADAD and BCBC meet at QQ, and the lines ABAB and CDCD meet at RR. Prove that the lines PQP Q and PRP R form the same angle as the diagonals of ABCDABCD.
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