Let Ω be the circumcircle of a triangle ABC with ∠BAC>90∘ and AB>AC. The tangents
of Ω at B and C cross at D and the tangent of Ω at A crosses the line BC at E. The line
through D, parallel to AE, crosses the line BC at F. The circle with diameter EF meets the
line AB at P and Q and the line AC at X and Y. Prove that one of the angles ∠AEB, ∠PEQ, ∠XEY is equal to the sum of the other two. RMM ShortlistgeometryRussian