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ABCD cyclic quadrilateral and 16 incenters

Source: Romanian IMO Team Selection Test TST 1996, problem 4

September 27, 2005
geometryincentercyclic quadrilateralgeometry unsolved

Problem Statement

Let ABCD ABCD be a cyclic quadrilateral and let M M be the set of incenters and excenters of the triangles BCD BCD , CDA CDA , DAB DAB , ABC ABC (so 16 points in total). Prove that there exist two sets K \mathcal{K} and L \mathcal{L} of four parallel lines each, such that every line in K∪L \mathcal{K} \cup \mathcal{L} contains exactly four points of M M .
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