What is the length of chord AB in circle O above? : Data Sufficiency (DS)

maxLRok

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

Updated on: 06 Dec 2012, 06:14

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A

B

C

D

E

Difficulty:

85% (hard)

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39% (01:30) correct

61% (01:23) wrong

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Chord.png [ 12.13 KiB | Viewed 10196 times ]

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

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

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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, theres 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 figure, its not possible to find the length of a chord from the measurements of the circle that contains it.

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Originally posted by maxLRok on 06 Dec 2012, 05:34.
Last edited by Bunuel on 06 Dec 2012, 06:14, edited 1 time in total.

Edited the question.

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BangOn

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Re: What is the length of chord AB in circle O above? [#permalink]

06 Dec 2012, 05:44

7

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.

maxLRok

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Joined: 26 Apr 2012

Posts: 34

Re: What is the length of chord AB in circle O above? [#permalink]

06 Dec 2012, 05:46

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!

BangOn

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Joined: 27 Feb 2012

Posts: 97

Re: What is the length of chord AB in circle O above? [#permalink]

06 Dec 2012, 05:49

1

Kudos

Its ok. Mistakes happen.
Press Kudos instead of thanks.

:)

joshlevin90

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Re: What is the length of chord AB in circle O above? [#permalink]

28 Mar 2014, 09:35

could some one explain why you cant make a triangle with the given information to find AB

L

Bunuel

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Re: What is the length of chord AB in circle O above? [#permalink]

28 Mar 2014, 09:46

1

Kudos

Expert Reply

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 9276 times ]

Hope it's clear.
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vietnammba

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Re: What is the length of chord AB in circle O above? [#permalink]

28 Oct 2014, 00:22

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?

L

Bunuel

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Joined: 02 Sep 2009

Posts: 92747

Re: What is the length of chord AB in circle O above? [#permalink]

28 Oct 2014, 03:57

2

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Expert Reply

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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earnit

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Re: What is the length of chord AB in circle O above? [#permalink]

10 Sep 2015, 18:56

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 ?

P

hellosanthosh2k2

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Re: What is the length of chord AB in circle O above? [#permalink]

30 Nov 2017, 12:55

Hi Bunuel, should we assume point O as center of circle?

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92747

Re: What is the length of chord AB in circle O above? [#permalink]

30 Nov 2017, 21:07

Expert Reply

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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amanvermagmat

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Location: India

Re: What is the length of chord AB in circle O above? [#permalink]

30 Nov 2017, 23:17

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?

P

amanvermagmat

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Joined: 22 Aug 2013

Posts: 1187

Location: India

Re: What is the length of chord AB in circle O above? [#permalink]

30 Nov 2017, 23:21

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).

B

kanhu1998

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Joined: 21 May 2021

Posts: 2

Re: What is the length of chord AB in circle O above? [#permalink]

11 Aug 2023, 04:45

Explanation: Statement (1) is insufficient. We don't know anything

about ABís position relative to OQ; remember that in Data Sufficiency, dia-
grams can be very misleading. While we know that A and B are on the circle

and AB intersects OQ at point P, that is all we know.
Statement (2) is also insufficient. This gives us a clearer relationship between
OQ and AB, but no distances, so there is no way to And the length of AB.
Taken together, the statements are sufficient. OA and OB are radiuses,
and since OQ = 5, OA = OB = 5. OAP and OBP are right triangles,
with a hypotenuse of 5 and one leg (OP) of 4. We can use the pythagorean
theorem, or our knowledge of the common triplet 3 : 4 : 5, to recognize that
AP = BP = 3. Thus, AB = 6. Choice (C) is correct.

B

hirakrintu

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

18 Aug 2023, 03:34

1

Kudos

Hi @Bunnel

Can you please explain why it is not "C" rather than "E" , As Pythagorean triplet (3,4,5) gives us sufficient information that OP is perpendicular to AB which thus bisects it (by theorem)

Regards,
Bishir

L

Bunuel

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Posts: 92747

Re: What is the length of chord AB in circle O above? [#permalink]

18 Aug 2023, 04:42

Expert Reply

hirakrintu wrote:

Hi @Bunnel

Can you please explain why it is not "C" rather than "E" , As Pythagorean triplet (3,4,5) gives us sufficient information that OP is perpendicular to AB which thus bisects it (by theorem)

Regards,
Bishir

The solution above is not correct. We don't know whether AB is perpendicular to OP, so we are not necessarily getting the right triangles.
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