# 7.     If the lines 3x – 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is         (a)    3/2(b)    3/4(c)    1/10(d)    1/20

Jitender Singh IIT Delhi
8 years ago
Ans:
Since both lines are parallel & tangent to the circle. Then distance between these two lines must be the diameter of the circle.
Lines:
$3x - 4y + 4 = 0$
$3x - 4y - \frac{7}{2} = 0$
Diameter ‘d’:
$d = \frac{|4-(-\frac{7}{2})|}{\sqrt{(3)^{2}}+(-4)^{2}} = \frac{\frac{15}{2}}{5} = \frac{3}{2}$
$\frac{3}{4}$