Question

The equations of four circles are (x ± a)² + (y ± a)² = a².

The radius of a circle touching all the four circles is

• A. ($\sqrt{2}$–1)a
• B. 2$\sqrt{2}$a
• C. ($\sqrt{2}$+ 1)a
• D. (2 + $\sqrt{2}$)a

Answer 1

Answer: (C)

($\sqrt{2}$+ 1)a

Answer 2

Radius of outer circle = a + a $\sqrt{2}$= ($\sqrt{2}$+ 1) a

Radius of inner circle = a $\sqrt{2}$– a = ($\sqrt{2}$–1) a