Let \Omega and \Gamma be circles with centres M and N, respectively, such that the radius of \Omega is less than the radius of \Gamma. Suppose \Omega and \Gamma intersect at two distinct points A and B. Line MN intersects \Omega at C and \Gamma at D, so that C, M, N, D lie on MN in that order. Let P be the circumcentre of triangle ACD. Line AP meets \Omega again at E\neq A and meets \Gamma again at F\neq A. Let H be the orthocentre of triangle PMN.
Prove that the line through H parallel to AP is tangent to the circumcircle of triangle BEF.
Proposed by Trần Quang Hùng, Vietnam