Math Problem Solver

Given a triangle ABC. Point F is the midpoint of the segment BC. The circumcircles passing through point A and tangent to the line BC at point F intersect the lines AB and AC at points M and N, respectively. The lines CM and BN intersect at point X. Point P is the intersection of the circumcircles of the triangles BMX and CNX. Prove that the points A, F, and P lie on the same line.