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Question

If a circle C passing through the point (4,0) touches the circle x2+y2+4x6y=12 externally at the point (1,1) then the radius of C is :

A
57
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B
4
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C
25
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D
5
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Solution

The correct option is D 5
Equation of tangent T, at point (1,1) is
x(1)+y(1)+2(x+1)3(y1)12=0
3x4y=7
Required circle is
(x1)2+(y+1)2+λ(3x4y7)=0 (1)
which passes through (4,0)
9+1+λ(127)=0
λ=2
From equation (1)
x2+y28x+10y+16=0
Radius =16+2516=5

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