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Prove that $P$, $A$, and $Q$ are collinear.

Source: Moldova TST 2022

April 1, 2022
geometry

Problem Statement

Let Ω\Omega be the circumcircle of triangle ABCABC such that the tangents to Ω\Omega in points BB and CC intersect in PP. The squares ABB1B2ABB_1B_2 and ACC1C2ACC_1C_2 are constructed on the sides ABAB and ACAC in the exterior of triangle ABCABC, such that the lines B1B2B_1B_2 and C1C2C_1C_2 intersect in point QQ. Prove that PP, AA, and QQ are collinear.
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