Given a triangle ABC. Let Ω be the circumscribed circle of this triangle, and ω be the inscribed circle of this triangle. Let δ be a circle that touches the sides AB and AC, and also touches the circle Ω internally at point D. The line AD intersects the circle Ω at two points P and Q (P lies between A and Q). Let O and I be the centers of the circles Ω and ω. Prove that OD∥IQ. geometrycircumcirclemixtilinearincircleChampions Tournament