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Question

The radius of the smallest circle which touches the straight-line 3xy=6 at (1,3) and also touches the line y=x is
(Compute upto one place of decimal only)

A
2 units
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B
1.5 units
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C
1.8 units
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D
1.2 units
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Solution

The correct option is B 1.5 units
3xy=6 and y=x touches the same circles and are not parallel to each other
So, we can say that tangents are drawn from a point P to the circles
P(3,3)
Now length of the tangent is
L=(31)2+(3+3)2=210 units
Now if the angle between the line 2θ half angle between the lines
tan2θ=2tanθ1tan2θ311+3=2tanθ1tan2θtanθ=±52
for acute angle tanθ=52
Now tanθ=rL
52=r210r=1024101.5 units

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