MathDB
parallel wanted, incircle, circumcircle and mixtlinear related

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2015 Seniors p3

September 3, 2020
geometrycircumcirclemixtilinearincircleChampions Tournament

Problem Statement

Given a triangle ABCABC. Let Ω\Omega be the circumscribed circle of this triangle, and ω\omega be the inscribed circle of this triangle. Let δ\delta be a circle that touches the sides ABAB and ACAC, and also touches the circle Ω\Omega internally at point DD. The line ADAD intersects the circle Ω\Omega at two points PP and QQ (PP lies between AA and QQ). Let OO and II be the centers of the circles Ω\Omega and ω\omega. Prove that OD∥IQOD \parallel IQ.
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