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Part of 2006 Estonia Math Open Junior Contests

Problems(1)

Estonian Math Competitions 2005/2006

Source: Juniors Problem 2

Let ABCD be a parallelogram, M the midpoint of AB and N the intersection of CD and the angle bisector of ABC. Prove that CM and BN are perpendicular iff AN is the angle bisector of DAB.

geometryparallelogramangle bisectorgeometry unsolved