Find radius of Circle There is a circle C1 of Radius R1 and another circle C2 of radius R2 (R2 ≤ R1) such that it touches circle C1 internally
 There is another circle C3 with radius R3 such that it touches the circle C1 from inside and the circle C2 from outside (it is given that R3 + R2 ≤ R1)
 Now there is a circle C4 of radius R4 which will touch the circles C2 and C3 externally and the circle C1 internally, let's call it as C4. It is guaranteed that such a set of circles can be drawn.
After drawing the four circles, the figure may look something like this: 

 Now we have to draw a circle C5 which will touch the circles C2 and C4 externally and the circle C1 internally. Circles C5 and C3 are not the same. We have to find the radius R5 of this circle using the information given
 In short Radii of C1,C2,C3,C4 are given then find the radius of Circle C5

You have just to apply Descartes' theorem.
Assuming that $R_i$ is the radius of $C_i$ and $\kappa_i=\frac{1}{R_i}$, $\kappa_4$ and $\kappa_5$ are given by:
$$ \kappa_1+\kappa_2+\kappa_3\pm 2\sqrt{\kappa_1\kappa_2+\kappa_1\kappa_3+\kappa_2\kappa_3},$$
so:
$$ \kappa_4+\kappa_5 = 2(\kappa_1+\kappa_2+\kappa_3). $$
