Triangle of 2 Arcs

Geometry Level 5

One big and one small circle share the same center OO.

Then ABC\triangle ABC is constructed such that points AA and BB are on the big circle while point CC is on the smaller circle. ABAB intersects the smaller circle at DD and EE and ACAC passes through FF and OO, as shown above.

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

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