Geometry GMAT, GRE Problem

The figure above shows three tangent circles (they touch at exactly one point), each with their centers along the same horizontal axis. The biggest circle contains two smaller ones. Of the two smaller circles, the larger one has a radius of 6 inches and the smaller one has a radius of 3 inches. What is the area of the shaded region?

A. 45π
B. 27π
C. 24π
D. 18π
E. 9π



A shaded region is the area of large semi-circle - the sum of areas of two smaller semi-circles

The sum of diameters of the two smaller circles = 6*2 + 3*2 = 18 = diameter of the large circle
The radius of the large circle = 9
The area of large circle =π∗9^2=81π

Sum of areas of two smaller circles π∗6^2+π∗32=45π

Shaded region 81π/2−45π/2=36π/2=18π

D