The radius of any circle touching the lines $3 x - 4 y + 5 = 0$ and $6 x - 8 y - 9 = 0$ is

1.9

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0.95

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2.9

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1.45

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Solution

The correct option is B $0.95$
Given lines $3 x - 4 y + 5 = 0$ and $3 x - 4 y - \frac{9}{2} = 0$
which are parallel to each others
$∴$ Perpendicular distance
$d = ∣ ∣ ∣ ∣ ∣ ∣ \frac{5 + \frac{9}{2}}{\sqrt{3^{2} + 4^{2}}} ∣ ∣ ∣ ∣ ∣ ∣ = \frac{19}{10}$
$∴$ Radius of circle $= \frac{d}{2} = \frac{19}{20} = 0.95$

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