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Angle Bisector at intersection of circumcircles

Source: Netherlands IMO TST 2019 P2

March 30, 2019
geometryangle bisectorcircumcircle

Problem Statement

Let ΔABC\Delta ABC be a triangle with an inscribed circle centered at II. The line perpendicular to AIAI at II intersects ⊙(ABC)\odot (ABC) at P,QP,Q such that, PP lies closer to BB than CC. Let ⊙(BIP)∩⊙(CIQ)=S\odot (BIP) \cap \odot (CIQ) =S. Prove that, SISI is the angle bisector of ∠PSQ\angle PSQ
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