Let ABC be a triangle with ∠A=120∘, I be the incenter, and M be the midpoint of BC. The line passing through M and parallel to AI meets the circle with diameter BC at points E and F (A and E lie on the same semiplane with respect to BC). The line passing through E and perpendicular to FI meets AB and AC at points P and Q respectively. Find the value of ∠PIQ. geometrySharygin Geometry OlympiadSharygin 2023Angle Chasing