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605-655 (Medium)|   Geometry|      
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In the diagram above, points A, B, C, D, and E all lie on the same lin 13 Feb 2017, 08:01
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68% (02:29) correct 32% (02:27) wrong based on 167 sessions

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In the diagram above, points A, B, C, D, and E all lie on the same line. Point B is the center of a smaller circle, on which points A and D lie. Point C is the center of a larger circle, on which points A and E lie. If the straight-line distance from point C to point D is two meters and the straight-line distance from point D to point E is 8 meters, what percentage of the larger circle is filled by the smaller circle?

A. 16%
B. 25%
C. 36%
D. 50%
E. 64%

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C
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In the diagram above, points A, B, C, D, and E all lie on the same lin 13 Feb 2017, 20:04
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CD = 2; DE = 8

CE = AC = 10

Area of smaller circle = pi*(AD/2)^2 = 36pi

Area of larger circle = pi*(AC)^2 = 100pi

Smaller circle occupies (36pi/100pi)*100 = 36% of larger circle.

Answer: C
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In the diagram above, points A, B, C, D, and E all lie on the same lin 14 Feb 2017, 06:22
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larger circle radius = 8 + 2 = 10

inner circle diameter = 10 + 2 = 12 => radius = 6

larger circle area = 100 pi

smaller circle area = 36 pi

there for 36 %

option C
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In the diagram above, points A, B, C, D, and E all lie on the same lin 30 Dec 2017, 02:01
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hazelnut

In the diagram above, points A, B, C, D, and E all lie on the same line. Point B is the center of a smaller circle, on which points A and D lie. Point C is the center of a larger circle, on which points A and E lie. If the straight-line distance from point C to point D is two meters and the straight-line distance from point D to point E is 8 meters, what percentage of the larger circle is filled by the smaller circle?

A. 16%
B. 25%
C. 36%
D. 50%
E. 64%

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VERITAS PREP OFFICIAL SOLUTION:

The key here is labeling everything that you know. If you know that:

DE = 8

CD = 2

and C is the center of the large circle

Then you can identify that the radius of the large circle is the distance from C to E which is 10, making the area of that circle equal to 100pi.

Then look at the smaller circle. You know that the distance from C to A is the radius of the larger circle, and you've already established that that distance is 10. And if CD is 2, that means that the diameter of the smaller circle is AC + CD (the total distance from A to D) for a total of 12. Since area is based on radius, cut that in half to a radius of 6, meaning that the area is 36pi.

Then, since you want to know what percentage the small circle takes up of the large circle, that's 36 pi out of 100 pi, for a total of 36%.
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In the diagram above, points A, B, C, D, and E all lie on the same lin 06 Jan 2022, 04:02
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