单选题
In the figure below, three circles of radius 1 are tangent to one another. What is the area of the shaded region between them?
【正确答案】
D
【答案解析】Use TACTIC 4 and add some lines: connect the centers of the three circles to form an equilateral triangle whose sides are 2.
[*]
Now use TACTIC 5 and find the shaded area by subtracting the area of the three sectors from the area of the triangle. The area of the triangle is[*](see Section 14-J). Each sector is one sixth of a circle of radius 1. Together they form one half of such a circle, so their total area is [*]. Finally subtract: the shaded area is [*]
[*]
Now use TACTIC 5 and find the shaded area by subtracting the area of the three sectors from the area of the triangle. The area of the triangle is[*](see Section 14-J). Each sector is one sixth of a circle of radius 1. Together they form one half of such a circle, so their total area is [*]. Finally subtract: the shaded area is [*]