Question

It the lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to a circle, then find the radius of circle.

Answer 1

Equation of tangents-

$3x-4y+4=0\dots \left(1\right)$

$6x-8y=7=0$

$\Rightarrow 3x-4y-\frac{7}{2}=0\dots \left(2\right)$

Since both tangents are parallel so distance between the tangents is the diameter of circle

Let radius of circle is $r$

$\therefore 2r=AB$

$\Rightarrow 2r=\frac{|4+\frac{7}{2}|}{\sqrt{3^2+(-4{)}^2}}$

$\Rightarrow 2r=\frac{15/2}{5}$

$\Rightarrow 2r=\frac{15}{5\times 2}$

$\Rightarrow r=\frac{3}{4}$

$\therefore$ Radius of circle is $\frac{3}{4}$