JBMO-SL 2007 G3

Let the inscribed circle of the triangle $\vartriangle ABC$ touch side $BC$ at $M$ , side $CA$ at $N$ and side $AB$ at $P$ . Let $D$ be a point from $\left[ NP \right]$ such that $\frac{DP}{DN}=\frac{BD}{CD}$ . Show that $DM \perp PN$ .