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

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

KEAMKEAM 2003

Solution:

Distance between the lines $ 3x-4y+5=0 $ and $ 6x-8y-9=0 $ is $ \left| \frac{5+\frac{9}{2}}{\sqrt{{{3}^{2}}+{{4}^{2}}}} \right|=\left( \frac{19}{10} \right)=1.9 $ is the diameter of circle $ \therefore $ Radius of circle $ =\frac{1.9}{2}=0.95 $