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circumscribed quadrilateral wanted, midpoint and 2 excenters related

Source: 2021 Saudi Arabia Training Lists p24 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 6, 2022
geometryexcenter

Problem Statement

Let ABCABC be triangle with MM is the midpoint of BCBC and X,YX, Y are excenters with respect to angle B,CB,C. Prove that MXMX, MYMY intersect ABAB, ACAC at four points that are vertices of circumscribed quadrilateral.
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