MathDB
super nice 6-th problem, an interesting result.

Source: Third Zhautykov Olympiad, Kazakhstan, 2007

April 25, 2007
geometrycircumcircletrapezoidtrigonometrygeometric transformationhomothetyratio

Problem Statement

Let ABCDEFABCDEF be a convex hexagon and it`s diagonals have one common point MM. It is known that the circumcenters of triangles MAB,MBC,MCD,MDE,MEF,MFAMAB,MBC,MCD,MDE,MEF,MFA lie on a circle. Show that the quadrilaterals ABDE,BCEF,CDFAABDE,BCEF,CDFA have equal areas.
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