I found this problem somewhere else. Im not happy with the solutions. I had a crack at it and im trying to show that |X'N|=|XM|. If i can do this then i can conclude AM=BN. Any help on solving this problem would be nice thanks.

P is a midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN