The tangent to the circle $C_1=x^2+y^2-2x-1=0$ at the point $(2,1)$ cuts off a chord of length 4 from a circle $C_2$ whose centre is $(3,-2)$. The radius of $C_2$ 

is

Equation of tangent to circle $x^2+y^2-2x-1=0$

at the point $(2,1)$ is $S_1=0$ $\Rightarrow x+y-3=0$

This line is chord of circle $C_2$

$OC=\frac{|3-2-3|}{\sqrt{2}}=\sqrt{2}$

$\therefore$ radius of circle is $\sqrt{C{A}^2+O{C}^2}=\sqrt{4+2}=\sqrt{6}$