If $2x-4y=9$and $6x-12y+7=0$ are parallel tangents to circle, then radius of the circle, is  

The equations of two tangents are $2x-4y-9=1$ and $6x-12y+7=0$. Clearly, these are parallel. The distance between these lines is  

$\left|\frac{-9-7}{\sqrt{4+16}}\right|=\frac{17}{3\sqrt{5}}$            $\left[\text{ Using }:d=\frac{\left|c_1-c_2\right|}{\sqrt{a^2+b^2}}\right]$

$\therefore$   Radius of the circle $=\frac{1}{2}\times \frac{17}{3\sqrt{5}}=\frac{17}{6\sqrt{5}}$