Let ΔABC be a triangle with an inscribed circle centered at I. The line perpendicular to AI at I intersects ⊙(ABC) at P,Q such that, P lies closer to B than C. Let ⊙(BIP)∩⊙(CIQ)=S. Prove that, SI is the angle bisector of ∠PSQ geometryangle bisectorcircumcircle