IKMC 2015 - Grades 11-12 - Self-study Question 16

Question 16

The figure shows three concentric circles and two perpendicular common diameters. The three grey sections have equal areas. The smallest circle has radius 1. What is the product of all three radii?

Question illustration

$\sqrt6$
$3$
$3\sqrt3/2$
$2\sqrt2$
$6$