2011年AMC10竞赛A第18题
2011年$$AMC10$$竞赛$$A$$第$$18$$题  Circles $$A$$, $$B$$, and $$C$$ each have radius $$1$$. Circles $$A$$ and $$B$$ share one point of tangency. Circle $$C$$ has a point of tangency with the midpoint of $$\overline{AB}$$. What is the area inside Circle $$C$$ but outside circle $$A$$ and circle $$B$$?  圆 $$A$$、$$B$$ 和 $$C$$ 的半径都是 $$1$$。 圆 $$A$$ 和 $$B$$ 有一个公共点。 圆 $$C$$ 与 $$\overline{AB}$$ 的中点有一个切点。 $$C$$ 圆内并且在$$A$$ 圆外和$$B$$ 圆外的面积是多少？
美国AMC10/12->Knowledge Point->Geometry->Calculation of Plane Geometry->Circle 课内体系->知识点->三角函数->三角函数的概念->任意角与弧度制->弧长公式与扇形面积
Not specific: Draw a rectangle with vertices at the centers of $$A$$ and $$B$$ and the intersection of $$A$$, $$C$$ and $$B$$, $$C$$. Then, we can compute the shaded area as the area of half of $$C$$ plus the area of the rectangle minus the area of the two sectors created by $$A$$ and $$B$$. This is $$\dfrac{\pi(1)^{2}}{2}+(2)(1)-2 \cdot \dfrac{\pi(1)^{2}}{4}= (\rm C)2$$. 