Let O be the circumcenter of the triangle ABC,A′ be a point symmetric of A wrt line BC,X is an arbitrary point on the ray AA′ (X=A). Angle bisector of angle BAC intersects the circumcircle of triangle ABC at point D (D=A). Let M be the midpoint of the segment DX. A line passing through point O parallel to AD, intersects DX at point N. Prove that angles BAM and CAN angles are equal. geometryangle bisectorequal anglescircumcircle