Question

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

• A. 3/2
• B. ¾
• C. 1/10
• D. 1/20

Answer 1

Answer: (B)

¾

Answer 2

Since both tangents are parallel to each other. The diameter of the circle is perpendicular distance between the parallel lines (tangents) $3 x - 4 y - \frac { 7 } { 2 } = 0$ and so it is equal to $\frac { 4 } { \sqrt { 9 + 16 } } + \frac { 7 / 2 } { \sqrt { 9 + 16 } } = \frac { 3 } { 2 }$.

Hence radius of circle is$\frac { 3 } { 4 }$.

Alternative method : Perpendicular distance =

$\frac { 3 ( 0 ) - 4 ( 1 ) - 7 / 2 } { 5 } = \frac { 3 } { 2 }$,

i.e., Diameter = $\frac { 3 } { 2 }$

Hence radius of circle is $\frac { 3 } { 4 }$