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TS EAMCET · Maths · Circle

If a diameter of the circle \(x^2+y^2-4 x+6 y-12=0\) is a chord of a circle \(S\) whose centre is at \((-3,2)\), then the radius of \(S\) is

  1. A \(5 \sqrt {3}\)
  2. B \(4 \sqrt {3}\)
  3. C \(2 \sqrt {3}\)
  4. D \(5\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(5 \sqrt {3}\)

Step-by-step Solution

Detailed explanation

\(r=\sqrt{(2)^2+(-3)^2+12}=\sqrt{25}=5\) \(O C=\sqrt{(2+3)^2+(-3-2)^2}=5 \sqrt{2}\) \(\begin{array}{ll}\therefore & O P^2=r^2+O C^2=25+50=75 \\ \Rightarrow & O P=\sqrt{75}=5 \sqrt{3} .\end{array}\)