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Orthogonal circles in bicentric polygon

Source: Sharygin 2017 Day 2 Problem 10.7 Grade 10

August 2, 2017
geometry

Problem Statement

10.7 A quadrilateral ABCDABCD is circumscribed around the circle ω\omega centered at II and inscribed into the circle Γ\Gamma. The lines AB,CDAB, CD meet at point PP, and the lines BC,ADBC, AD meet at point QQ. Prove that the circles ⊙(PIQ)\odot(PIQ) and Γ\Gamma are orthogonal.
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