Triangles and circles?

Geometry Level 3

Consider a triangle ΔABC \Delta ABC. Drop a perpendicular BEBE from BB to ACAC. Now drop a perpendicular CFCF from CC to ABAB. Point of intersection of BEBE and CFCF is OO.

Given that AFOEAFOE lie on a circle of radius 55 units and CAB=60 \angle CAB = 60^{\circ}. Find the radius of circle which passes through the points A,B A,B and CC.

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