Question 891679
Note that the figure formed is an equilateral, equiangular, triangle with side 2r and interior angles of 60 degrees.  For each circle, the area of the intercepted sector is {{{A[s] = (pi/6)*r^2}}}
==> the combined area of the sectors is {{{3*A[s] = (pi/2)*r^2}}}.

But the area of the equilateral triangle with side 2r is 
{{{sqrt(3)*r^2}}}, hence

{{{16.13 = sqrt(3)*r^2 - (pi/2)*r^2}}}
<==> {{{16.13/(sqrt(3) - pi/2) = r^2}}}
==> {{{sqrt(16.13/(sqrt(3) - pi/2)) = r}}}
Then r = 10.00141131, or practically, r = 10 units.