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  4. If one of the diameters of the circle x2 + y2 - 2x - 6y + 6 = 0 is a chord to the circle with centre (2,1), then the radius of the circle is

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Q. If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord to the circle with centre $(2,1)$, then the radius of the circle is

IIT JEEIIT JEE 2004Conic Sections

Solution:

Here, radius of sm aller circle, AC = $\sqrt{1 + 9- 6} = 2$
Clearly, from the figure the radius of bigger circle
$r^2 = 2^2 + [(2 - 1)^2 + (1 - 3)^2] $
$r^2=9 \Rightarrow r = 3 $

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