Let ABC be a triangle with circumcircle ω and let ΩA be the A-excircle. Let X and Y be the intersection points of ω and ΩA. Let P and Q be the projections of A onto the tangent lines to ΩA at X and Y respectively. The tangent line at P to the circumcircle of the triangle APX intersects the tangent line at Q to the circumcircle of the triangle AQY at a point R. Prove that AR⊥BC. geometrycircumcircleexcircleDDITISL 2021