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01 Jul 2024, 11:23
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
99% (01:54) correct
0% (00:00) wrong based on 7 sessions
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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?
A. \(\frac{\sqrt{2}}{2}r^2\)
B. \(\frac{\sqrt{3}}{2}r^2\)
C. \(\sqrt{2}r^2\)
D. \(\sqrt{3}r^2\)
E. \(2\sqrt{3}r^2\)
Attachment:
GMAT-Club-Forum-2xhfmtde.jpeg [ 23.86 KiB | Viewed 243 times ]
17 Oct 2024, 13:49
Kudos
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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 \(\frac{\sqrt{3}}{2r}\), 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.
3.jpg [ 62.33 KiB | Viewed 512 times ]
1.jpg [ 31.17 KiB | Viewed 514 times ]
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 \(\frac{\sqrt{3}}{2r}\), 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.
Attachment:
3.jpg [ 62.33 KiB | Viewed 512 times ]
Attachment:
1.jpg [ 31.17 KiB | Viewed 514 times ]
