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BC, a midpoint and a point on the median are concyclic

Source: Italian National Olympiad 2007, problem 3

May 13, 2007
geometrycircumcirclerhombustrapezoidparallelogramgeometry proposed

Problem Statement

Let ABC be a triangle, G its centroid, M the midpoint of AB, D the point on the line AGAG such that AG=GD,A≠DAG = GD, A \neq D, E the point on the line BGBG such that BG=GE,B≠EBG = GE, B \neq E. Show that the quadrilateral BDCM is cyclic if and only if AD=BEAD = BE.
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