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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



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


Grade:10

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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}
Radius:
\frac{3}{4}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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