2. 职称英语
  3. [img]2014m9x/ct_egreqm_egreqjs_0053_20148[/img]In the figure above, O and P are

[img]2014m9x/ct_egreqm_egreqjs_0053_20148[/img]In the figure above, O and P are

游客2024-01-12  15
问题
In the figure above, O and P are the centers of the two circles. If each circle has radius r, what is the area of the shaded region?
选项 A、 
B、 
C、 
D、 
E、 
答案 B
解析 If a geometric problem contains a figure, it can be helpful to draw additional lines and add information given in the text of the problem to the figure. For circles, the helpful additional lines are often radii or diameters. In this case, drawing radius OP will divide the shaded region into two triangles, as shown in the figure below.

The two circles have the same radius, r. Therefore, in each of the triangles, all three sides have length r, and each of the triangles is equilateral. If you remember from geometry that the height of an equilateral triangle with sides of length r is, you could use that fact in solving the problem. However, if you do not remember what the height is, you can use the following figure to help you find the height.

Using the Pythagorean theorem, you get

So the area of the equilateral triangle is 1/2(base)(height)=. Since the shaded region consists of 2 equilateral triangles with sides of length r, the area of the shaded region is(2), and the correct answer is Choice B.
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