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Three concurrent lines in a configuration with two circles

Source: Japan TST 2022, Day 2, P3

September 17, 2022
geometry

Problem Statement

Given is a circle Γ\Gamma with diameter MNMN and a point AA inside Γ\Gamma. The circle with center NN, passing through AA, meets Γ\Gamma at BB and CC. Let P,Q∈BCP, Q \in BC, such that ∠BAP=∠QAC\angle BAP= \angle QAC. The lines NP,NQNP, NQ meet Γ\Gamma at X,YX, Y, respectively. Prove that AM,PY,QXAM, PY, QX are concurrent.
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