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In the ﬁgure above, the diameter of the circle is 10.
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12 Dec 2015, 06:49
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#GREpracticequestion The area of quadrilateralABCD.jpg [ 9.19 KiB | Viewed 7808 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
Expert Reply
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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Brent Hanneson – Creator of greenlighttestprep.com Sign up for GRE Question of the Dayemails
Re: In the ﬁgure above, the diameter of the circle is 10.
[#permalink]
27 Apr 2020, 13:22
GreenlightTestPrep wrote:
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
RELATED VIDEO
why do we need to change the shape? cant we calculate the values as per the given diagram?
_________________
Re: In the ﬁgure above, the diameter of the circle is 10.
[#permalink]
27 Apr 2020, 13:30
2
Expert Reply
Farina wrote:
why do we need to change the shape? cant we calculate the values as per the given diagram?
What values are you referring to? All we're told is that the diameter of the circle is 10. Other than the fact that the quadrilateral is inscribed in the circle, there's no other information that will "lock in" the area of the quadrilateral. As such, we need to consider various possible scenarios.
Cheers, Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com Sign up for GRE Question of the Dayemails