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  3. [img]ct_gre5image016[/img]The circles above, with centers O and P, each have ra

[img]ct_gre5image016[/img]The circles above, with centers O and P, each have ra

游客2025-02-24  14
问题
The circles above, with centers O and P, each have radius r.

Column A                                             Column B
Twice the area of the shaded region.                 The area of the circular region with center P.   
选项 A、if the quantity in Column A is greater
B、if the quantity in Column B is greater
C、if the two quantity are equal
D、if the relationship cannot be determined from the information given
答案 A
解析 上面图中以O，P为圆心的圆的半径均为r
解：本题的正确答案为(A)。由图可和P点在圆O上，而O点在圆P上，过点O作圆P的切线，由该切线把阴影区分为两部分：半圆+剩余部分。因为两圆面积相同，所以比较左项=2×(半圆的面积+剩余部分的面积)=圆P的面积+2×剩余部分的面积。由此可知比较左项显然大于比较右项。
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