Triangles and circles?

Geometry Level 3

Consider a triangle \( \Delta ABC\). Drop a perpendicular \(BE\) from \(B\) to \(AC\). Now drop a perpendicular \(CF\) from \(C\) to \(AB\). Point of intersection of \(BE\) and \(CF\) is \(O\).

Given that \(AFOE\) lie on a circle of radius \(5\) units and \( \angle CAB = 60^{\circ}\). Find the radius of circle which passes through the points \( A,B\) and \(C\).