VN-TST 2002 Problem 1

Find all triangles $ABC$ for which $\angle ACB$ is acute and the interior angle bisector of $BC$ intersects the trisectors $(AX, (AY$ of the angle $\angle BAC$ in the points $N,P$ respectively, such that $AB=NP=2DM$ , where $D$ is the foot of the altitude from $A$ on $BC$ and $M$ is the midpoint of the side $BC$ .