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QP bisects <AQC

Source: : Rioplatense 2017 L3 P5

September 19, 2022
geometryangles

Problem Statement

Let ABCABC be a triangle and II is your incenter, let PP be a point in ACAC such that PIPI is perpendicular to ACAC, and let DD be the reflection of BB wrt circumcenter of △ABC\triangle ABC. The line DIDI intersects again the circumcircle of △ABC\triangle ABC in the point QQ. Prove that QPQP is the angle bisector of the angle ∠AQC\angle AQC.
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