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Source: 43rd International Tournament of Towns, Senior A-Level P5, Fall 2021 & Kvant Magazine No. 11-12 2021 M2676

February 18, 2023
geometryTournament of TownsKvant

Problem Statement

Let ABCDABCD be a parallelogram and let PP{} be a point inside it such that ∠PDA=∠PBA\angle PDA= \angle PBA. Let ω1\omega_1 be the excircle of PABPAB opposite to the vertex AA{}. Let ω2\omega_2 be the incircle of the triangle PCDPCD. Prove that one of the common tangents of ω1\omega_1 and ω2\omega_2 is parallel to ADAD.
Ivan Frolov
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