Question 136
Let $ABCD$ be an isosceles trapezoid such that $AB = 17$, $BC = DA = 25$, and $CD = 31$. Points $P$ and $Q$ are selected on sides $AD$ and $BC$, respectively, such that $AP = CQ$ and $PQ = 25$. Suppose that the circle with diameter $PQ$ intersects the sides $AB$ and $CD$ at four points which are vertices of a convex quadrilateral. Compute the area of this quadrilateral.