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# Cyclic Hexagon

Six points $$A, B, C, D, E, F$$ all lie on the circumference of a circle $$\Gamma$$ in a clockwise direction, such that $$AB=BC$$, $$CD=DE$$ and $$EF=FA$$. Lines $$FC$$, $$AD$$ and $$BE$$ intersect at point $$O$$ inside the circle. Prove that triangles $$FAO$$, $$ABO$$, $$BCO$$, $$CDO$$, $$DEO$$ and $$EFO$$ are isosceles triangles.

Note by Julian Poon
3 months, 3 weeks ago