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Points A, B, and C are three different points on a circle, which has a

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Points A, B, and C are three different points on a circle, which has a [#permalink] New post   06 May 2021, 04:17
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Points A, B, and C are three different points on a circle, which has area equal to \(64\pi.\)

Quantity A
Quantity B
AB+AC
32



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.

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Points A, B, and C are three different points on a circle, which has a [#permalink] New post   06 May 2021, 08:36
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Solution:

Area of the circle=π\(r^2\).
64π=π\(r^2\)
r=8

Thus, if AB/AC is on the diameter it can be 16.
But both of them cannot be on the diameter and one of them has to be less than 16.
Making the sum of the two less than 32

Qty A< Qty B

IMO B

Hope this helps!
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Re: Points A, B, and C are three different points on a circle, which has a [#permalink] New post   06 May 2021, 20:35
Ks1859 wrote:
Solution:

Area of the circle=π\(r^2\).
64π=π\(r^2\)
r=8

Thus, if AB/AC is on the diameter it can be 16.
But both of them cannot be on the diameter and one of them has to be less than 16.
Making the sum of the two less than 32

Qty A< Qty B

IMO B

Hope this helps!


i understand your reasoning but, the info only said 3 point of circle and nothing else
from that we can consider there may two diameter or two chords or one diameter and one chord....shouldn't ans be option D not sufficient into to reach one result
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Points A, B, and C are three different points on a circle, which has a [#permalink] New post   06 May 2021, 22:01
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void wrote:
Ks1859 wrote:
Solution:

Area of the circle=π\(r^2\).
64π=π\(r^2\)
r=8

Thus, if AB/AC is on the diameter it can be 16.
But both of them cannot be on the diameter and one of them has to be less than 16.
Making the sum of the two less than 32

Qty A< Qty B

IMO B

Hope this helps!


i understand your reasoning but, the info only said 3 point of circle and nothing else
from that we can consider there may two diameter or two chords or one diameter and one chord....shouldn't ans be option D not sufficient into to reach one result


Hi there!

There cannot be 2 diameter. There can only be one diameter in one circle(Considering tha there are only three point). And diameter is the longest chord so, the other chord on the circle will be shorter that the diameter. Thus is does not matter whether we have 2 chord or 1 diameter and one chord. Therefore Qty A will always be less than Qty B.

Hope this helps

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Re: Points A, B, and C are three different points on a circle, which has a [#permalink] New post   07 May 2021, 02:12
void wrote:
Ks1859 wrote:
Solution:

Area of the circle=π\(r^2\).
64π=π\(r^2\)
r=8

Thus, if AB/AC is on the diameter it can be 16.
But both of them cannot be on the diameter and one of them has to be less than 16.
Making the sum of the two less than 32

Qty A< Qty B

IMO B

Hope this helps!


i understand your reasoning but, the info only said 3 point of circle and nothing else
from that we can consider there may two diameter or two chords or one diameter and one chord....shouldn't ans be option D not sufficient into to reach one result


The option would have been 'D' if we were given four points : A, B, C, D instead of three. In case of four points, you can create 2 diameters in the circle. The idea is that you can only have one diameter from a single point on the circle
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Re: Points A, B, and C are three different points on a circle, which has a [#permalink] New post   07 May 2021, 10:33
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Area of circle = pi*r^2 = 64*pi
=> r = 8
Maximum length of a chord in a circle is the diameter.whose length = 8*2=16
For A, B, C being three different points in the circle.
Only one of either AB or AC can be the diameter, and the other one will be less than the diameter.

Quantity B = 2*diameter = 32.

Thus, A < B.
Option (B)
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Re: Points A, B, and C are three different points on a circle, which has a [#permalink] New post   11 May 2021, 14:28
I think its not clear at all, what happened if we take ab and ac as arcs?
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Re: Points A, B, and C are three different points on a circle, which has a [#permalink] New post   11 May 2021, 23:26
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FCOCGALVAN wrote:
I think its not clear at all, what happened if we take ab and ac as arcs?


Hi there!

I think in GRE we do not have to make out of the box assumptions. The question seems pretty straightforward.

Let me know if I can help you further.

Regards

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Points A, B, and C are three different points on a circle, which has a [#permalink] New post   11 May 2021, 23:28
FCOCGALVAN wrote:
I think its not clear at all, what happened if we take ab and ac as arcs?


Hi there!

I think in GRE we do not have to make out of the box assumptions. The question seems pretty straightforward. Even if they are arcs they can be joined with a straight line.

Ps.: Did you know? That a circle is made when you join many such straight lines.

Let me know if I can help you further.

Regards
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Re: Points A, B, and C are three different points on a circle, which has a [#permalink] New post   26 Mar 2025, 07:07
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Re: Points A, B, and C are three different points on a circle, which has a [#permalink]
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