The lengths of the tangents from P(1,-1) and Q(3,3) to a circle are $\sqrt{2}$ and  $\sqrt{6}$ respectively, then the length of the tangents from R(-1,-5) to the same circle is 

Let the given circle be 
 $x^2+y^2+2gx+2fy+c=0$
Let the tangents drawn from P, Q and R touch the circle at A,B and C respectively then
$P{A}^2=2\_\_\_\left(1\right)$ , $P{B}^2=6\_\_\_\left(2\right)$ using length of tangent formula,
solving (1) and(2) 
 $$\begin{gathered} g=-1-\frac{c}{3};f=-1+\frac{c}{6} \\ R{C}^2=1+25-2g-10f+c=38 \\ \therefore RC=\sqrt{38} \end{gathered}$$