Christmas Contest Individual Round Tiebreaker

Let \triangle ABC be acute-angled with \angle ABC = 35^\circ. Suppose that I is the incenter of \triangle ABC and that AI +AC = BC. Let P be the point such that PB and PC are tangent to the circumcircle of \triangle ABC. Let Q be the point on the line AB such that PQ is parallel to AC. Find \angle AQC in degrees.