Rectangle \(ABCD\) is given with \(AB=63\) and \(BC=448.\) Points \(E\) and \(F\) lie on \(AD\) and \(BC\) respectively, such that \(AE=CF=84.\) The inscribed circle of triangle \(BEF\) is tangent to \(EF\) at point \(P,\) and the inscribed circle of triangle \(DEF\) is tangent to \(EF\) at point \(Q.\) Find \(PQ.\)
(第二十五届AIME2 2007 第9题)