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Points M such that AM/BM=CM/DM - Iran NMO 2006 - Problem5

Source:

September 23, 2010
geometrycircumcircleangle bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a convex cyclic quadrilateral. Prove that: a)a) the number of points on the circumcircle of ABCDABCD, like MM, such that MAMB=MDMC\frac{MA}{MB}=\frac{MD}{MC} is 44. b)b) The diagonals of the quadrilateral which is made with these points are perpendicular to each other.
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