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
- A \(\sqrt{41} \mathrm{~cm}\)
- B \(\sqrt{11} \mathrm{~cm}\)
- C \(\sqrt{21} \mathrm{~cm}\)
- D \(\sqrt{31} \mathrm{~cm}\)
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 \(\triangle C A B\),…
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