Problem 2.  Let Ω and Γ be circles with centres M and N , respectively, such that the radius of Ω is less than the radius of Γ . Suppose Ω and Γ intersect at two distinct points A and B . Line MN intersects Ω at C and Γ 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 Ω again at E ≠ A and meets Γ again at F ≠ 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 .