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Prove that M ≡ D - [Bulgaria NMO 2010]

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May 19, 2010
geometrytrapezoidgeometric transformationincenterinradiusgeometry unsolved

Problem Statement

Let kk be the circumference of the triangle ABC.ABC. The point DD is an arbitrary point on the segment AB.AB. Let II and JJ be the centers of the circles which are tangent to the side AB,AB, the segment CDCD and the circle k.k. We know that the points A,B,IA, B, I and JJ are concyclic. The excircle of the triangle ABCABC is tangent to the side ABAB in the point M.M. Prove that M≡D.M \equiv D.
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