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TS EAMCET · Maths · Circle

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

  1. A 6
  2. B 4
  3. C 2
  4. D 3
Verified Solution

Answer & Solution

Correct Answer

(D) 3

Step-by-step Solution

Detailed explanation

Equation of circle \( x^2+y^2-2 x-6 y+6=0 \) Centre \((1,3), r=\sqrt{1+9-6}=2\) \( \begin{aligned} O A & =\sqrt{(2-1)^2+(1-3)^2} \Rightarrow O A=\sqrt{1+4}=\sqrt{5} \\ \because A B & =r=2 \text { and } R^2=r^2+O A^2 \\ \Rightarrow R^2 & =4+5 \Rightarrow R=3 \end{aligned} \)