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# What is the length of chord AB in circle O above?

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Intern
Joined: 26 Apr 2012
Posts: 34
What is the length of chord AB in circle O above? [#permalink]

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06 Dec 2012, 04:34
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Difficulty:

95% (hard)

Question Stats:

39% (01:22) correct 61% (01:00) wrong based on 214 sessions

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Chord.png [ 12.13 KiB | Viewed 5573 times ]
What is the length of chord AB in circle O above?

(1) OQ = 5
(2) OP = 3

[Reveal] Spoiler:
Gmat Hacks Challenge Problem found in the Data Sufficiency Challenge set, I thought the answer was "C" because if you know OQ than you can draw a line to OA and form a right triangle and than if you have the heigh OP you can find the missing side (AP) which is half of AB.

OA:
34. E
Explanation: Most measurements in a circle (radius, diameter, circumference, area) are closely related, but the same is not true of chords. Statement (1) is not sufficient, as knowing the length of the radius tells us nothing about the length of the chord, which could be placed anywhere between the top of the circle and just above the center. Statement (2) is also insufficient even if we know the placement of point P on the radius, theres no way to use that to find the length of the chord.

Taken together, we still have little information about chord AB. Unless the chord is part of a quadrilateral, triangle, or other figure, its not possible to find the length of a chord from the measurements of the circle that contains it.
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Dec 2012, 05:14, edited 1 time in total.
Edited the question.
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Joined: 27 Feb 2012
Posts: 136
Re: What is the length of chord AB in circle O above? [#permalink]

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06 Dec 2012, 04:44
4
KUDOS
What is the length of chord AB in circle O above?
(1) OQ = 5
(2) OP = 3

E. Your reference that OQ is perpendicular to AB is incorrect.
The perpendicular from center of circle on a chord bisects the chord.
Just looking at figure and figuring that it is perpendicular is incorrect.

Hope its clear.
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Intern
Joined: 26 Apr 2012
Posts: 34
Re: What is the length of chord AB in circle O above? [#permalink]

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06 Dec 2012, 04:46
1
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BangOn wrote:
What is the length of chord AB in circle O above?
(1) OQ = 5
(2) OP = 3

E. Your reference that OQ is perpendicular to AB is incorrect.
The perpendicular from center of circle on a chord bisects the chord.
Just looking at figure and figuring that it is perpendicular is incorrect.

Hope its clear.

Wow stupid mistake on my part. Thank you!
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Joined: 27 Feb 2012
Posts: 136
Re: What is the length of chord AB in circle O above? [#permalink]

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06 Dec 2012, 04:49
Its ok. Mistakes happen.
:)
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Intern
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Posts: 4
Re: What is the length of chord AB in circle O above? [#permalink]

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28 Mar 2014, 08:35
could some one explain why you cant make a triangle with the given information to find AB
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: What is the length of chord AB in circle O above? [#permalink]

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28 Mar 2014, 08:46
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Expert's post
joshlevin90 wrote:
could some one explain why you cant make a triangle with the given information to find AB

Not sure which triangle you are taking about...

As for the answer: all we know even when we combine the statements is the radius of the circle (r=OQ=5) and the positioning of point P on OQ (OP=3). We know nothing about the chord AB other than it passes through point P: it can be at any angle to OQ, which gives different values of its length.
Attachment:

Untitled.png [ 12.16 KiB | Viewed 4748 times ]

Hope it's clear.
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Re: What is the length of chord AB in circle O above? [#permalink]

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27 Oct 2014, 23:22
Bunuel wrote:
joshlevin90 wrote:
could some one explain why you cant make a triangle with the given information to find AB

Not sure which triangle you are taking about...

As for the answer: all we know even when we combine the statements is the radius of the circle (r=OQ=5) and the positioning of point P on OQ (OP=3). We know nothing about the chord AB other than it passes through point P: it can be at any angle to OQ, which gives different values of its length.
Attachment:
Untitled.png

Hope it's clear.

Hi Bunuel,

In case OQ bisects AB, is the answer C?
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: What is the length of chord AB in circle O above? [#permalink]

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28 Oct 2014, 02:57
2
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Expert's post
vietnammba wrote:
Bunuel wrote:
joshlevin90 wrote:
could some one explain why you cant make a triangle with the given information to find AB

Not sure which triangle you are taking about...

As for the answer: all we know even when we combine the statements is the radius of the circle (r=OQ=5) and the positioning of point P on OQ (OP=3). We know nothing about the chord AB other than it passes through point P: it can be at any angle to OQ, which gives different values of its length.
Attachment:
Untitled.png

Hope it's clear.

Hi Bunuel,

In case OQ bisects AB, is the answer C?

"Bisect" means to divide into two equal parts. So, AB bisects OQ at P, means that OP = PQ = 2.5. In this case the answer would still be E, because the angle at which AB cuts OQ would still be unknown.

But if we were told that AB is perpendicular to OQ, then the answer would be C.

Hope it's clear.
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Re: What is the length of chord AB in circle O above? [#permalink]

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10 Sep 2015, 17:56
In case OQ bisects AB, is the answer C?[/quote]

"Bisect" means to divide into two equal parts. So, AB bisects OQ at P, means that OP = PQ = 2.5. In this case the answer would still be E, because the angle at which AB cuts OQ would still be unknown.

But if we were told that AB is perpendicular to OQ, then the answer would be C.

Hope it's clear.[/quote]

In reference to the highlighted portion, isn't it possible to solve the question if we just know the radius OQ.
30, 30, 120 with a distribution of x, x, x$$\sqrt{3}$$ for the triangle OAB ?
Senior Manager
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Re: What is the length of chord AB in circle O above? [#permalink]

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30 Nov 2017, 11:55
Hi Bunuel, should we assume point O as center of circle?
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: What is the length of chord AB in circle O above? [#permalink]

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30 Nov 2017, 20:07
hellosanthosh2k2 wrote:
Hi Bunuel, should we assume point O as center of circle?

The question assumes that O is the centre. But proper GMAT question would mention this clearly. Anyway since the answer is E it does not matter here.
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Re: What is the length of chord AB in circle O above? [#permalink]

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30 Nov 2017, 22:17
earnit wrote:
In case OQ bisects AB, is the answer C?

"Bisect" means to divide into two equal parts. So, AB bisects OQ at P, means that OP = PQ = 2.5. In this case the answer would still be E, because the angle at which AB cuts OQ would still be unknown.

But if we were told that AB is perpendicular to OQ, then the answer would be C.

Hope it's clear.[/quote]

In reference to the highlighted portion, isn't it possible to solve the question if we just know the radius OQ.
30, 30, 120 with a distribution of x, x, x$$\sqrt{3}$$ for the triangle OAB ?[/quote]

Hi

How would you know that its a 30-30-120 triangle only, just from the statement that AB is perpendicular to OQ?
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Re: What is the length of chord AB in circle O above? [#permalink]

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30 Nov 2017, 22:21
vietnammba wrote:
Bunuel wrote:
joshlevin90 wrote:
could some one explain why you cant make a triangle with the given information to find AB

Not sure which triangle you are taking about...

As for the answer: all we know even when we combine the statements is the radius of the circle (r=OQ=5) and the positioning of point P on OQ (OP=3). We know nothing about the chord AB other than it passes through point P: it can be at any angle to OQ, which gives different values of its length.
Attachment:
Untitled.png

Hope it's clear.

Hi Bunuel,

In case OQ bisects AB, is the answer C?

Hi

If its given in the question that O is the center of the circle, and its also given that OQ bisects AB, then by the theorem, OQ will be perpendicular to AB also. Then when we combine the two statements, we have right triangle OPB, where radius OB and OP are known;- thus we can get PB. And thus we can get AB also (double of PB).
Re: What is the length of chord AB in circle O above?   [#permalink] 30 Nov 2017, 22:21
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