Answer
$C(r) = \frac{2\pi x}{\sqrt3}$
Work Step by Step
In equilateral triangle, circumcenter, incenter coincide
So OA is also angle bisector.
This gives $r = \frac{x}{\sqrt3}$
Now circumference of circle = $C(r) = 2\pi r$ = $2\pi\frac{x}{\sqrt3}$
$C(r) = \frac{2\pi x}{\sqrt3}$
