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In the figure above, x=2. What is the area of circle O?[img]2011q3/ct_egmatqj_eg
In the figure above, x=2. What is the area of circle O?[img]2011q3/ct_egmatqj_eg
游客
2024-01-14
50
管理
问题
In the figure above, x=2. What is the area of circle O?
选项
A、
B、
C、
D、
E、
答案
B
解析
Since we are looking for the area of the circle, we really need to find the radius. The line segment from the center of the circle to the vertex of the square is 2, so we can use that to find the radius. If you extend line x to the opposite vertex of the square, you have drawn a diagonal of that square, which is also the hypotenuse of a 45°-45°-90° triangle. The diagonal measures 4. You normally multiply a leg of a 45°-45°-90° triangle by
to get the hypotenuse, so we have to divide the hypotenuse by
to get the leg (which is also the side of the square and the diameter of the circle). Therefore, the diameter is equal to
and the radius is equal to
. But we’re not done; we still have to find the area. The formula for the area of a circle is A=nr2, so we have to substitute
in for r. Squaring both the top and bottom of the fraction, we get 4/2 , or 2. So the area of the circle is 2π.
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