Let $R$ be the radius of the large circle and $r$ be the radius of any of the 3 smaller circles.
If you draw an equilateral triangle between the three points of intersection of the smaller and large circles you can work out that
$r = \dfrac{\sqrt{3}}{2+\sqrt{3}}R$
see if that helps you work out the rest.
while Skeeter is a wonder I didn't think his math intuition was supernatural so I figured this must be a known problem and sure enough...
https://owlcation.com/stem/Solution-...ircles-Problem