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If one of the diameter 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 bigger circle is
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Verified Answer
The correct answer is:
3
Equation of circle
$$
x^2+y^2-2 x-6 y+6=0
$$
Centre $(1,3), r=\sqrt{1+9-6}=2$
$$
\begin{aligned}
O A & =\sqrt{(2-1)^2+(1-3)^2} \Rightarrow O A=\sqrt{1+4}=\sqrt{5} \\
\because A B & =r=2 \text { and } R^2=r^2+O A^2 \\
\Rightarrow R^2 & =4+5 \Rightarrow R=3
\end{aligned}
$$
$$
x^2+y^2-2 x-6 y+6=0
$$
Centre $(1,3), r=\sqrt{1+9-6}=2$
$$
\begin{aligned}
O A & =\sqrt{(2-1)^2+(1-3)^2} \Rightarrow O A=\sqrt{1+4}=\sqrt{5} \\
\because A B & =r=2 \text { and } R^2=r^2+O A^2 \\
\Rightarrow R^2 & =4+5 \Rightarrow R=3
\end{aligned}
$$
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