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A smaller circle is inscribed in a larger circle shown as ab

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by Max@Math Revolution » Sun Apr 03, 2016 2:07 am
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A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle's area?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6


* A solution will be posted in two days.
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by GMATinsight » Sun Apr 03, 2016 5:21 am
Max@Math Revolution wrote:Image

A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle's area?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6


* A solution will be posted in two days.
From Figure we see that

radius of bigger circle = Diameter of smaller circle

Let, Radius of Bigger circle = 2 = Diameter of smaller circle

i.e. Radius of Smaller circle = 2/2 = 1

Area of Bigger circle = Pi 2^2 = 4 Pi
Area of Smaller circle = Pi 1^2 = Pi

Area of Shaded Region = Big circle - Small Circle = 4 Pi - Pi = 3Pi

Shaded Area/Area of Big circle = 3Pi/4 Pi = 3/4

Answer: Option C
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by Max@Math Revolution » Tue Apr 05, 2016 4:58 am
A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle's area?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6


-> As the ratio of the radius is 1:2, the ratio of the area is 1:4.
If the area of the small circle is a, the shaded area is 3a.
Thus, 3a/(a+3a)=3/4 and the answer is C.
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