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

Arun Kumar IIT Delhi
6 years ago
Hello Student,
Since both lines are parallel & tangent to the circle. Then distance between these two lines must be the diameter of the circle.
Lines:
$3x - 4y + 4 = 0$
$3x - 4y - \frac{7}{2} = 0$
$\frac{3}{4}$$d = \frac{|4-(-\frac{7}{2})|}{\sqrt{(3)^{2}}+(-4)^{2}} = \frac{\frac{15}{2}}{5} = \frac{3}{2}$
R=d/2
Thanks & Regards
Arun Kumar
Btech, IIT Delhi