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.
(第十八届AIME2 2000 第10题)