Question 13
Let I be the center of the incircle γ of triangle ABC and O its circumcenter. Let $\omega _A$ be the circle through B,C tangent to γ. Define $\omega _B$,$\omega _C$ similarly. Let A′ be the other intersection of $\omega _B$,$\omega _C$, and define B′,C′ similarly. Prove that AA′,BB′,CC′ concur at a point K collinear with O and I.