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Problem 2 of Third round

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

December 24, 2019
geometry

Problem Statement

Let ABCDABCD be an inscribed quadrilateral and PP be an inner point for it so that ∠PAB=∠PBC=∠PCD=∠PDA\angle PAB=\angle PBC=\angle PCD=\angle PDA. The lines ADAD and BCBC intersect in point QQ and lines ABAB and CDCD – in point RR. Prove that ∠(PQ,PR)=∠(AC,BD)\angle (PQ,PR)=\angle (AC,BD).
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