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Bulgarian National Olympiad 2018 Day 2 P4

Source:

April 15, 2018
geometry

Problem Statement

Let ABCDABCD be a quadrilateral ,circumscribed about a circle. Let MM be a point on the side ABAB. Let I1I_{1},I2I_{2} and I3I_{3} be the incentres of triangles AMDAMD, CMDCMD and BMCBMC respectively. Prove that I1I2I3MI_{1}I_{2}I_{3}M is circumscribed.
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