# Triangle of 2 Arcs

Geometry Level 5

One big and one small circle share the same center $$O$$.

Then $$\triangle ABC$$ is constructed such that points $$A$$ and $$B$$ are on the big circle while point $$C$$ is on the smaller circle. $$AB$$ intersects the smaller circle at $$D$$ and $$E$$ and $$AC$$ passes through $$F$$ and $$O$$, as shown above.

If $$AF = 3$$ (red segment), $$DE = 6$$ (blue segment), and $$BC = 11$$ (green side), what is the radius of the smaller, orange circle?

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