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Proving the equilateral triangle

Source: Turkey National Mathematical Olympiad 2019 P4

December 23, 2019

geometry

Problem Statement

In a triangle

\Delta ABC

,

|AB|=|AC|

. Let

M

be on the minor arc

AC

of the circumcircle of

\Delta ABC

different than

A

and

C

. Let

BM

and

AC

meet at

E

and the bisector of

\angle BMC

and

BC

meet at

F

such that

\angle AFB=\angle CFE

. Prove that the triangle

\Delta ABC

is equilateral.

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