A point P is chosen inside a triangle ABC with circumcircle Ω. Let Γ be the circle passing
through the circumcenters of the triangles APB, BPC, and CPA. Let Ω and Γ intersect at
points X and Y. Let Q be the reflection of P in the line XY . Prove that ∠BAP=∠CAQ. Isogonal conjugategeometryRMM Shortlist