Let A B C be a triangle with incenter I, and let D be the foot of the angle bisector from A to B C. Let \Gamma be the circumcircle of triangle B I C, and let P Q be a chord of \Gamma passing through D. Prove that A D bisects \angle P A Q.
Let A B C be a triangle with incenter I, and let D be the foot of the angle bisector from A to B C. Let \Gamma be the circumcircle of triangle B I C, and let P Q be a chord of \Gamma passing through D. Prove that A D bisects \angle P A Q.