Question

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

• A. $7$
• B. $\frac{7}{2}$
• C. $\frac{7}{4}$
• D. $\frac{7}{6}$

Answer 1

The correct option is C $\frac{7}{4}$

Given lines can be written as, $3x+4y=14$ and $3x+4y=-\frac{7}{2}$

Clearly both the lines are parallel

Hence radius $=\frac{1}{2}$ distance between the lines $=\frac{1}{2}\frac{14+\frac{7}{2}}{\sqrt{3^2+4^2}}=\frac{7}{4}$