Problem

Source: JBMO Shortlist 2013, G4

Tags: incenter, circumcircle, excircle, geometry, perpendicular



Let I be the incenter and AB the shortest side of the triangle ABC. The circle centered at I passing through C intersects the ray AB in P and the ray BA in Q. Let D be the point of tangency of the A-excircle of the triangle ABC with the side BC. Let E be the reflection of C with respect to the point D. Prove that PECQ.