As the three friends sitting at equal distance , that means the string form an equilateral triangle and the center of circle is the centroid of the triangle.
Let the side of the equilateral triangle be a units
then, by pythagoras theorem ,
the length perpendicular = a√3/2
and centroid divides the perpendicular in 2 :1 ratio.
so, radius = 2a√3/6
⇒20 = a/√3
⇒a = 20√3 m
length of string = 3× 20√3 = 60√3 m
= 103.92 m