If the lines $3 x+4 y-14=0$ and $6 x+8 y+7=0$ are both tangents to a circle, then its radius is

Question

Aicharya · Accepted Answer

Given, lines

are both tangents to a circle we observe that, both lines are parallel i.e., $\begin{aligned} 3 x+4 y-14 & =0 \\ 3 x+4 y+\frac{7}{2} & =0 \end{aligned}$ So, radius of circle $=\frac{1}{2}$ (distance between two parallel lines) $\begin{aligned} & =\frac{1}{2}\left\{\frac{|7 / 2+14|}{\sqrt{9+16}}\right\} \\ & =\frac{1}{2}\left\{\frac{35 / 2}{5}\right\}=\frac{1}{2} \times \frac{7}{2} \\ & =\frac{7}{4}\end{aligned}$

If the lines $3 x+4 y-14=0$ and $6 x+8 y+7=0$ are both tangents to a circle, then its radius is

Solution