MathDB

3

Part of 2007 ITAMO

Problems(1)

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

Source: Italian National Olympiad 2007, problem 3

5/13/2007
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.
geometrycircumcirclerhombustrapezoidparallelogramgeometry proposed