IKMC 2008 - Grades 11-12 - Self-study Question 15

Question 15

Three circles of radius r touch externally as shown. Find the area of the central region A.

1. $(\sqrt3-\pi/2)r^2$
2. $(\pi/2-\sqrt3/2)r^2$
3. $\pi r^2/8$
4. $(\sqrt3-3/2)\pi r^2$
5. $(\pi/3-\sqrt3/2)r^2$