Let M, N and P be midpoints of sides BC,AC and AB, respectively, and let O be circumcenter of acute-angled triangle ABC. Circumcircles of triangles BOC and MNP intersect at two different points X and Y inside of triangle ABC. Prove that ∠BAX=∠CAY. geometrycircumcircletrigonometryratiosymmetrygeometric transformationreflection