MathNet 2007-part-02 — 187 problems (EN–VI) Question 91

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