MEMO 2013 I3

Let $ABC$ be an isosceles triangle with $AC=BC$ . Let $N$ be a point inside the triangle such that $2 \angle ANB = 180 ^\circ + \angle ACB$ . Let $D$ be the intersection of the line $BN$ and the line parallel to $AN$ that passes through $C$ . Let $P$ be the intersection of the angle bisectors of the angles $CAN$ and $ABN$ . Show that the lines $DP$ and $AN$ are perpendicular.