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equal segments wanted, 2 circumcircles and 2 excirles given

Source: BMO Shortlist 2018 G1

May 5, 2019
geometryBalkan MO Shortlist

Problem Statement

Let ABCABC be an acute triangle and let MM be the midpoint of side BCBC. Let D,ED,E be the excircles of triangles AMB,AMCAMB,AMC respectively, towards MM. Circumcirscribed circle of triangle ABDABD intersects line BCBC at points BB and FF. Circumcirscribed circles of triangle ACEACE intersects line BCBC at points CC and GG. Prove that BF=CGBF=CG.
by Petru Braica, Romania
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