\( P \) is an interior point of triangle \( A B C \) such that AP, BP, CP meet BC, CA, AB at \( D, E, F \) respectively. Let \( M \) and \( N \) be points on segments BF and \( C E \) respectively so that \( B M: M F=E N: N C \). Let \( M N \) meet \( B E \) and \( C F \) at \( X \) and \( Y \) respectively. Prove that \( M X: Y N=B D \) : \( D C \).
