Question

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

• A. $ \frac{3}{4}$
• B. $ \frac{2}{3}$
• C. $ \frac{1}{4}$
• D. $ \frac{5}{2}$

Answer 1

Answer: (A)

The diameter of the circle is perpendicular distance between the parallel lines (tangents)
$3x - 4y + 4 = 0$ and
$\frac{4}{\sqrt{9+16}}+\frac{7/2}{\sqrt{9+16}}=\frac{3}{2}$. Hence radius is $\frac{3}{4}.$