Let ABC be an acute-angled triangle with circumcircle ω. A circle Γ is internally tangent to ω at A and also tangent to BC at D. Let AB and AC intersect Γ at P and Q respectively. Let M and N be points on line BC such that B is the midpoint of DM and C is the midpoint of DN. Lines MP and NQ meet at K and intersect Γ again at I and J respectively. The ray KA meets the circumcircle of triangle IJK again at X=K.Prove that ∠BXP=∠CXQ.Kian Moshiri, United Kingdom IMO ShortlistgeometryISL 2023