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TS EAMCET · Maths · Circle

A circle with centre at \((2,4)\) is such that the line \(x+y+2=0\) cuts a chord of length 6 . The radius of the circle is

  1. A \(\sqrt{41} \mathrm{~cm}\)
  2. B \(\sqrt{11} \mathrm{~cm}\)
  3. C \(\sqrt{21} \mathrm{~cm}\)
  4. D \(\sqrt{31} \mathrm{~cm}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{41} \mathrm{~cm}\)

Step-by-step Solution

Detailed explanation

Let \(r\) be the radius of the circle. Now, perpendicular distance \[ \begin{aligned} A C & =\frac{|2+4+2|}{\sqrt{1^2+1^2}}=\frac{8}{\sqrt{2}} \\ & =4 \sqrt{2} \end{aligned} \] In right angled \(\triangle C A B\),…