Suppose that $ D,E,F$ are points on sides $ BC,CA,AB$ of a triangle $ ABC$ respectively such that $ BD=CE=AF$ and $ \angle BAD=\angle CBE=\angle ACF$.Prove that the triangle $ ABC$ is equilateral.
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Tags: geometry unsolved, geometry
Suppose that $ D,E,F$ are points on sides $ BC,CA,AB$ of a triangle $ ABC$ respectively such that $ BD=CE=AF$ and $ \angle BAD=\angle CBE=\angle ACF$.Prove that the triangle $ ABC$ is equilateral.