The radius of any circle touching the lines \( \Large 3x-4y+5=0\ and\ 6x-8y-9=0 \) is:

A) 1.9

B) 0.95

C) 2.9

D) 1.45

Correct answer:
B) 0.95

Description for Correct answer:

Since, given lines are parallel to each other so the line segment joining the points of contact is diameter of the circle, distance between the lines

\( \Large 3x-4y+5=0\ and\ 3x-4y-\frac{9}{2}=0\ is \)

\( \Large |\frac{5+\frac{9}{2}}{\sqrt{3^{2}+4^{2}}}|\ =\ |\frac{9}{10}| = 1.9 \)

Length of diameter of the circle is 1.9.

Radius of circle = \( \Large \frac{1.9}{2} = 0.95 \)



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