How do you find the radius? Can someone tell me how you can find the radius of the circle in the figure given below:

Given:
$$RS = WS$$
I have tried all I know but I just dont understand how can you use only information related to angles to find the length of the radius.
 A: Set $S = (0,0)$, and  W.L.O.G. assume that the vertical coordinate of W and R is the same. Thus $W = (\sqrt{3}L/2,L/2)$ and $R = (-\sqrt{3}L/2,L/2)$, with $L = RS=SW$.
Because $R,S$ and $W$ are points on a circle $(x-a)^2+(y-b)^2 = r^2$, the following equations should be satisfied
$$ (0-a)^2+(0-b)^2 = r^2$$
$$ (\sqrt{3}L/2-a)^2+(L/2-b)^2 = r^2$$
$$ (-\sqrt{3}L/2-a)^2+(L/2-b)^2 = r^2$$
From the two last equations, we have $a=0.$ Thus, we will have the system
$$ b^2 = r^2 $$
$$ 3L^2/4 +(L/2-b)^2 = r^2,$$
which gives $r = L.$
A: Connect points $R,S,W$ to the center of the circle $C$. Note that the triangles $RCS$ and $SCW$ are congruent and isosceles (as two out of three sides are equal to the radius). Thus, angles $RSC$ and $WSC$ are equal and must be of $60^0$. Hence, all angles in both triangles are the same $(60^0)$, and the radius = $RS = WS$. 
A: Thinking out loud:
Using the information from Find the radius from a sector, and knowing that a central angel is 2 times the angle given, I reached this solution.
I am not sure it is correct though, but I don't know what is wrong with it if it is incorrect.

