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)