Triangle of 2 Arcs

Geometry Level 5

One big and one small circles 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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