Hello ukorovIn the attached diagram, I have marked the points of contact with the smaller circle as E and F.

Then, if the radius of the smaller circle isand if , then (tangents from a point to a circle are equal)

In cm (Pythagoras)

Solving these simultaneous equations: .

So the radius of the smaller circle is cm.

Similarly let and

Express the lengths of and in terms of and . Then use the fact that to form another equation. Solve these equations to find , the radius of the larger circle.

Grandad