Question 16
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.
Show that the lines $DP$ and $AN$ are perpendicular.