Let $$AB$$ be a diameter of a circle $$C_1$$ of radius $$30\ \text{cm}$$ and with center $$O$$. Two circles $$C_2$$ and $$C_3$$ of radii $$15\ \text{cm}$$ and $$10\ \text{cm}$$ touch $$C_1$$ internally at $$A$$ and $$B$$ respectively. A fourth circle $$C_4$$ touches $$C_1$$, $$C_2$$ and $$C_3$$. What is the largest possible radius of $$C_4$$?

A

$$12\ \text{cm}$$

B

$$15\ \text{cm}$$

C

$$20\ \text{cm}$$

D

$$30\ \text{cm}$$