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2007 JBMO TST- Macedonia, problem 2

Source: 2007 JBMO TST- Macedonia

May 28, 2019
JuniorMacedoniaJMMO2007geometryparallelogram

Problem Statement

Let ABCDABCD be a parallelogram and let EE be a point on the side ADAD, such that AEED=m\frac{AE}{ED} = m. Let FF be a point on CECE, such that BF⊥CEBF \perp CE, and the point GG is symmetrical to FF with respect to ABAB. If point AA is the circumcenter of triangle BFGBFG, find the value of mm.
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