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 $C$ .