<Tri-2024-2158>, hint

Suppose AP cut the circumcircle of OBPC  in D.

Since  in triangle ABY, <BAY=90-A <ABY=90, <AYB=<A  and <BCP=<BDP=<A

AYBD are cyclic and <ADY=<ABY=90. Similarly <ADX=90

Hence AP ㅗ XY

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