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I, J and O are collinear - [Iran Second Round 1988]

Source:

December 7, 2010
geometryconicscyclic quadrilateralgeometry proposed

Problem Statement

In a cyclic quadrilateral ABCDABCD, let I,JI,J be the midpoints of diagonals AC,BDAC, BD respectively and let OO be the center of the circle inscribed in ABCD.ABCD. Prove that I,JI, J and OO are collinear.
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