

Geometry
Problem 990: Triangle, Incircle, Median, Cevian, Central
Angle, Congruence, Circle, Secant, Midpoint,
Parallel Lines.
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In a triangle ABC the median BM intersects
the incircle of center I at D and E, respectively (see the figure).
DJ is parallel to AC and angles DIH and JIE are equal (H and J on the incircle). BH and BJ
extended meet AC at F and G, respectively. Prove that AF = GC.







