IMO Shortlist 2017 problem G7


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A convex quadrilateral ABCD has an inscribed circle with center I. Let I_a, I_b, I_c and I_d be the incenters of the triangles DAB, ABC, BCD and CDA, respectively. Suppose that the common external tangents of the circles AI_bI_d and CI_bI_d meet at X, and the common external tangents of the circles BI_aI_c and DI_aI_c meet at Y. Prove that \angle{XIY}=90^{\circ}.

Izvor: https://www.imo-official.org/problems/IMO2017SL.pdf