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Inscribed circles in rectangle

Source: AIME II 2007 #9

March 29, 2007
geometryrectanglesymmetryAMCAIMEratiogeometric transformation

Problem Statement

Rectangle ABCDABCD is given with AB=63AB=63 and BC=448.BC=448. Points EE and FF lie on ADAD and BCBC respectively, such that AE=CF=84.AE=CF=84. The inscribed circle of triangle BEFBEF is tangent to EFEF at point P,P, and the inscribed circle of triangle DEFDEF is tangent to EFEF at point Q.Q. Find PQ.PQ.
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