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Part of 2017 Lusophon Mathematical Olympiad

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VII Lusophon Mathematical Olympiad 2017 - Problem 6

Source: VII Lusophon Mathematical Olympiad 2017 - Problem 6

7/29/2017
Let ABC be a scalene triangle. Consider points D, E, F on segments AB, BC, CA, respectively, such that AF‾\overline{AF}=DF‾\overline{DF} and BE‾\overline{BE}=DE‾\overline{DE}. Show that the circumcenter of ABC lies on the circumcircle of CEF.
geometrycircumcircle