The lines   and   are tangents to the same circle. The radius

of the circle is  then  _____(where m,n are relatively prime)

 

diameter = distance between parallel tangents

$\begin{array}{r}3x-4y+4=0\\ 6x-8y-7=0\Rightarrow 3x-4y-\frac{7}{2}=0\\ \text{ the given tangents are parallel. }\\ d=\frac{\left|c_2-c_1\right|}{\sqrt{a^2+b^2}}=\frac{\left|4-\left(-\frac{7}{2}\right)\right|}{\sqrt{3^2+(-4{)}^2}}=\frac{\left(\frac{15}{2}\right)}{\sqrt{9+16}}=\frac{15}{2\times 5}=\frac{3}{2}\\ \Rightarrow r=\frac{3}{4}\end{array}$