Question

If the lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to a circle of radius $r$, then the value of $4r$ is

Answer 1

Given lines are
$3x-4y+4=0$ and
$6x-8y-7=0\Rightarrow 3x-4y-\frac{7}{2}=0$
As both the lines are parallel, so the length of the diameter
$d=\frac{|4-(-\frac{7}{2})|}{5}\Rightarrow 2r=\frac{3}{2}\therefore 4r=3$