OMCPLP 2014 Problem 3

In a convex quadrilateral $ABCD$ , $P$ and $Q$ are points on sides $BC$ and $DC$ such that $B\hat{A}P = D\hat{A}Q$ . If the line that passes through the orthocenters of $\triangle ABP$ and $\triangle ADQ$ is perpendicular to $AC$ , prove that the area of these triangles are equals.