AMC10 2002 B

AMC10 2002 B · Q5

AMC10 2002 B · Q5. It mainly tests Circle theorems, Area & perimeter.

Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.

半径为 2 和 3 的圆外部相切，并被第三个圆外接，如图所示。求阴影区域的面积。

(A) $3\pi$ $3\pi$

(B) $4\pi$ $4\pi$

(D) $9\pi$ $9\pi$

(E) $12\pi$ $12\pi$

Answer

Correct choice: (E)

正确答案：（E）

Solution

(E) The diameter of the large circle is 6 + 4 = 10, so its radius is 5. Hence, the area of the shaded region is $\pi(5^2)-\pi(3^2)-\pi(2^2)=\pi(25-9-4)=12\pi.$

（E）大圆的直径是 $6+4=10$，所以半径是 $5$。因此，阴影部分的面积为 $\pi(5^2)-\pi(3^2)-\pi(2^2)=\pi(25-9-4)=12\pi.$

Topics