TH-TMO 2013 Problem 12

Let $\omega$ be the incircle of $\vartriangle ABC$ , $\omega$ is tangent to sides $BC$ and $AC$ at $D$ and $E$ respectively. The line perpendicular to $BC$ at $D$ intersects $\omega$ again at $P$ . Lines $AP$ and $BC$ intersect at $M$ . Let $N$ be a point on segment $AC$ so that $AE = CN$ . Line $BN$ intersects $\omega$ at $Q$ (closer to $B$ ) and intersect $AM$ at $R$ . Show that the area of $\vartriangle ABR$ is equal to the area of $PQMN$ .