TH-TMO 2007 Problem 3

A triangle $\vartriangle ABC$ has $\angle B = 90^o$ . A circle is tangent to $AB$ at $B$ and also tangent to $AC$ . Another circle is tangent to the first circle as well as the two sides $AB$ and $AC$ . Suppose that $AB =\sqrt3$ and $BC = 3$ . What is the radius of the second circle?