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Let ABCD be a circumscribed quadrilateral. Let g be a line through A which meets the segment BC in M and the line CD in N. Denote by I_1, I_2 and I_3 the incenters of \triangle ABM, \triangle MNC and \triangle NDA, respectively. Prove that the orthocenter of \triangle I_1I_2I_3 lies on g.

Proposed by Nikolay Beluhov, Bulgaria

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