Inspired from a recent post:
How does one obtain the radius of a circle that circumscribes an equilateral triangle with side length x?
knew that question would spark some interest.
Walker has a nice picture, but essentially the long side of the smaller triangle is x/2 then small side is xsqrt3/6
So the hypt. is xsqrt3/3 Which is the radius. or as walker puts it x/sqrt3