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One trick problem?!

Source: Sharygin Correspondence Round 2024 P23

March 6, 2024
geometrytransformationTangents

Problem Statement

A point PP moves along a circle Ω\Omega. Let AA and BB be two fixed points of Ω\Omega, and CC be an arbitrary point inside Ω\Omega. The common external tangents to the circumcircles of triangles APCAPC and BCPBCP meet at point QQ. Prove that all points QQ lie on two fixed lines.
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