Semi-circle $C_1$ is drawn with a line segment PQ as its diameter with centre at R. Semicircle $C_2$ and $C_3$ are drawn with PR and QR as diameters respectively, both $C_2$ and $C_3$ lying inside $C_1$. A full circle $C_4$ is drawn in such a way that it is tangent to all the three semicircle $C_1. C_2$ and $C_3. C_4$ lies inside $C_1$ and outside both $C_2$ and $C_3$. The radius of $C_4$ is