Question

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 find the value of $$ \frac{r_1 + r_2}{r}. $$

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

Hint:

Use symmetry and tangent circle properties for nested circle systems.

Answer 1

The Correct Option is C

By the problem's geometric configuration and known results for tangent circles in square arrangement, the sum of radii ratio is: \[ \frac{r_1 + r_2}{r} = 2\sqrt{2} \]