The following is problem 8 from a GRE exam found here.
The problem states that the two circles with radius $r=3$ intersect each other such that the area of the darkened region is equal to the sum of areas of the dashed regions. Find the area of the darkened region. Thanks.
Denote the area of the darkened region as $A$, and denote the area of each of the dashed regions as $B$. The areas of the dashed regions are equal since the two intersecting circles have equal area. So $A+B=\pi\cdot 3^2=9\pi$, since $A$ and $B$ added give the area of the circle with radius $3$. But based on given information, $A=2B$. Can you proceed from there?