A Series of Hard Problems (2 of 3)

A circle is inscribed in quadrilateral $ABCD$ , tangent to $\overline{AB}$ at $P$ and to $\overline{CD}$ at $Q$ . Given that $AP = 19$ , $PB=26$ , $CQ=37$ , and $QD=23$ , find the square of the radius of the circle.