AP EAMCET · Maths · Circle
If \(r_1\) and \(r_2\) are radii of two circles touching all the four circles \((x \pm r)^2+(y \pm r)^2=r^2\), then \(\frac{r_1+r_2}{r}=\)
- A \(\frac{\sqrt{2}+1}{2}\)
- B \(3 \sqrt{2}\)
- C \(2 \sqrt{2}\)
- D \(\frac{3+\sqrt{2}}{4}\)
Answer & Solution
Correct Answer
(C) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Distance from origin to center of any given circle: \(d = \sqrt{r^2+r^2} = r\sqrt{2}\). For inner circle (radius \(r_1\)) touching externally: \(r_1+r = d \Rightarrow r_1 = r\sqrt{2}-r\). For outer circle (radius \(r_2\)) touching internally:…
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