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ASU 504 All Soviet Union MO 1989 circumcenter of AEF lies on bisector of EDF

Source:

August 14, 2019
geometryCircumcenterequidistantangle bisector

Problem Statement

ABCABC is a triangle. Points D,E,FD, E, F are chosen on BC,CA,ABBC, CA, AB such that BB is equidistant from DD and FF, and CC is equidistant from DD and EE. Show that the circumcenter of AEFAEF lies on the bisector of EDFEDF.
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