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The circles shown are tangent at point B. Point A is the ce
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07 Mar 2018, 14:36
07 Mar 2018, 14:36
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95% (00:54) correct
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#GREpracticequestion The circles shown are tangent at point B.jpg [ 12.06 KiB | Viewed 13050 times ]
The circles shown are tangent at point B. Point A is the center of the larger circle, and line segment AB (not shown) is a diameter of the smaller circle. The area of the smaller circle is what fraction of the area of the larger circle?
enter your value
Show: :: OA
\(\frac{1}{4}\)
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Re: The circles shown are tangent at point B. Point A is the ce
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07 Mar 2018, 19:22
07 Mar 2018, 19:22
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Expert Reply
The fastest way to solve this problem is to know that for any two similar shapes, the ratio of their areas is equal to the square of the ratio of their lengths. For example, a square with a side of 5 and an area of 25, and a square with a side of 10 and an area of 100. The ratio of their side lengths is 1:2, but the ratio of their areas is 1:4.
In this problem, we can quickly see that the diameter of the small circle is half that of the larger circle. Squaring 1/2 gets us 1/4, so the small circle has 1/4 the area of the larger.
In this problem, we can quickly see that the diameter of the small circle is half that of the larger circle. Squaring 1/2 gets us 1/4, so the small circle has 1/4 the area of the larger.
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Re: The circles shown are tangent at point B. Point A is the ce
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02 May 2018, 07:49
02 May 2018, 07:49
Carcass wrote:
Attachment:
circles.jpg
The circles shown are tangent at point B. Point A is the center of the larger circle, and line segment AB (not shown) is a diameter of the smaller circle. The area of the smaller circle is what fraction of the area of the larger circle?
enter your value
Show: :: OA
\(\frac{1}{4}\)
Let's assign some values that meet the given conditions.
So, let's say that AB = 2
This means the RADIUS of the LARGE circle = 2
It also means that the DIAMETER of the SMALL circle = 2
If the DIAMETER of the SMALL circle = 2, then the RADIUS of the SMALL circle = 1
The area of the smaller circle is what fraction of the area of the larger circle?
Area = π(radius)²
So, area of BIG circle = π(2²) = 4π
And the area of SMALL circle = π(1²) = 1π
From here, we can see that the area of the smaller circle is 1/4 of the area of the larger circle (i.e., 1π is 1/4 of 4π)
Answer: 1/4
Cheers,
Brent
