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
Show Answer
Answer:
Correct Answer: 7. (a)
Solution:
- Here, radius of smaller circle, $A C=\sqrt{1^{2}+3^{2}-6}=2$
Clearly, from the figure the radius of bigger circle
$$ \begin{aligned} & r^{2}=2^{2}+\left[(2-1)^{2}+(1-3)^{2}\right] \\ & r^{2}=9 \quad \Rightarrow \quad r=3 \end{aligned} $$
