Let ABC be a triangle, I its incenter, and Γ its circumcircle. Let D be the second point of intersection of AI with Γ. The line parallel to BC through I intersects AB and AC at P and Q, respectively. The lines PD and QD intersect BC at E and F, respectively. Prove that triangles IEF and ABC are similar. geometrysimilaritycircumcircleincenter