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In the figure above, the diameter of the circle is 10. [#permalink]
12 Dec 2015, 06:49
Expert's post
00:00
Question Stats:
70% (00:48) correct
29% (00:57) wrong based on 48 sessions
Attachment:
#GREpracticequestion The area of quadrilateralABCD.jpg [ 9.19 KiB | Viewed 2695 times ]
In the figure above, the diameter of the circle is 10.
Quantity A
Quantity B
The area of quadrilateral ABCD
40
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Practice Questions Question: 3 Page: 151 Difficulty: medium
Re: In the figure above, the diameter of the circle is 10. [#permalink]
01 Oct 2019, 10:15
2
This post received KUDOS
Expert's post
Carcass wrote:
Attachment:
#GREpracticequestion The area of quadrilateralABCD.jpg
In the figure above, the diameter of the circle is 10.
Quantity A
Quantity B
The area of quadrilateral ABCD
40
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Practice Questions Question: 3 Page: 151 Difficulty: medium
First of all, it's important not to read too much into the diagram. All we can glean from the diagram is that we have a quadrilateral that is inscribed in the circle. That's it!
So, first recognize that the inscribed quadrilateral COULD be a very very very narrow rectangle like this. Notice that this quadrilateral COULD be so thin that its area is very very close to zero. So, for this particular quadrilateral we get: Quantity A: a very very small area that's close to zero Quantity B: 40 In this case, Quantity B is greater.
Alternatively, we COULD make the quadrilateral quite large. In fact, we could make it a SQUARE.
So, if the inscribed quadrilateral is a square, what is its area? To find out, let's draw a diagonal. One of our circle properties tells us that this diagonal must be the diameter of the circle, which we know is 10 To find the area of the square, we need to know the length of each side. So, let's let x = the length of each side.
Since ACD is a RIGHT TRIANGLE, we can apply the Pythagorean Theorem to get: x² + x² = 10² Simplify to get 2x² = 100 Divide both sides by 2 to get: x² = 50
This means the area of the square = 50 We know this because the area of the square = (x)(x) = x², and we just learned that x² = 50
So, for this particular quadrilateral we get: Quantity A: 50 Quantity B: 40 In this case, Quantity A is greater.
Answer: D
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Re: In the figure above, the diameter of the circle is 10.
[#permalink]
01 Oct 2019, 10:15
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70% (00:48) correct
