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AP EAMCET · Maths · Circle

The ratio of the areas of the greatest and the smallest circles touching \((x \pm 1)^2+(y \pm 1)^2=1\) is

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

Answer & Solution

Correct Answer

(C) \(\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}\)

Step-by-step Solution

Detailed explanation

(c) Let radius of smaller circle be \(r\) and radius of bigger.circle be \(R\) \(\begin{aligned} r & =\sqrt{2}-1 \\ R & =\sqrt{2}+1 \\ \therefore \text { Ratio of areas } & =\frac{(\sqrt{2}+1)^2}{(\sqrt{2}-1)^2}=\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}\end{aligned}\)