# 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 $C$.

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