Circle 2 Question 6

7. If one of the diameters of the circle $x^{2}+y^{2}-2 x-6 y+6=0$ is a chord to the circle with centre $(2,1)$, then the radius of the circle is $\quad(2004,1 M)$

(a) $\sqrt{3}$

(b) $\sqrt{2}$

(c) 3

(d) 2

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Answer:

Correct Answer: 7. (c)

Solution:

  1. Here, radius of smaller circle, $A C=\sqrt{1^{2}+3^{2}-6}=2$

Clearly, from the figure the radius of bigger circle

$ \begin{aligned} & r^{2}=2^{2}+\left[(2-1)^{2}+(1-3)^{2}\right] \\ & r^{2}=9 \quad \Rightarrow \quad r=3 \end{aligned} $



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