In a non-isosceles acute triangle ABC, D is the midpoint of the edge [BC]. The points E and F lie on [AC] and [AB], respectively, and the circumcircles of CDE and AEF intersect in P on [AD]. The angle bisector from P in triangle EFP intersects EF in Q. Prove that the tangent line to the circumcirle of AQP at A is perpendicular to BC. geometrycircumcircleangle bisector