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VII Lusophon Mathematical Olympiad 2017 - Problem 6

Source: VII Lusophon Mathematical Olympiad 2017 - Problem 6

July 29, 2017

geometrycircumcircle

Problem Statement

Let ABC be a scalene triangle. Consider points D, E, F on segments AB, BC, CA, respectively, such that

\overline{AF}

\overline{DF}

and

\overline{BE}

\overline{DE}

. Show that the circumcenter of ABC lies on the circumcircle of CEF.