Question

The lines $3x-4y=4$ and $6x-8y-7=0$ are tangents to the same circle. Then is radius is ?

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{3}{2}$

Answer 1

Answer: (A)

$\frac{1}{4}$

The equation of the given tangents are 3x−4y+4=03x−4y+4=0 and 6x−8y−7=0

The slopes of the given tangents are $\frac{3}{4}$

$HereC1=4andC2=-7/2$

$d=\left|\frac{4-(-\frac{7}{2})}{\sqrt{3^2+4^2}}\right|=\left|\frac{\frac{15}{2}}{5}\right|=\left|\frac{15}{10}\right|=\frac{3}{2}$

$diameter\frac{3}{2}unitsandradius\frac{3}{4}units$