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# Is arc ABC equal in length to arc DEF?

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Manager
Joined: 18 Oct 2010
Posts: 71
Is arc ABC equal in length to arc DEF?  [#permalink]

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31 May 2012, 05:26
2
14
00:00

Difficulty:

95% (hard)

Question Stats:

33% (01:31) correct 67% (01:11) wrong based on 308 sessions

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Attachment:

arc.JPG [ 6.11 KiB | Viewed 7709 times ]

Is arc ABC equal in length to arc DEF?

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Joined: 02 Sep 2009
Posts: 58445
Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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31 May 2012, 05:49
4
2
Joy111 wrote:
Attachment:
The attachment arc.JPG is no longer available

Is arc ABC equal in length to arc DEF?

Consider two cases below:
Attachment:

Arcs.png [ 13.11 KiB | Viewed 7647 times ]

Case 1: M is the center of the circle --> arc ABC = arc DEF;
Case 2: M is NOT the center of the circle --> arc ABC # arc DEF.
Not sufficient.

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##### General Discussion
Intern
Joined: 23 Apr 2014
Posts: 20
Is arc ABC equal in length to arc DEF?  [#permalink]

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Updated on: 28 May 2015, 07:56
Hi Bunuel got the stmt 1 that it is not sufficient but could you please explain stmt 2.. As the ad=cf doesnt it mean that they are the diameters

Originally posted by kasturi72 on 27 May 2015, 23:10.
Last edited by kasturi72 on 28 May 2015, 07:56, edited 1 time in total.
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Joined: 04 Jan 2015
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Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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28 May 2015, 03:18
2
kasturi72 wrote:
Hi Bunueli got the stmt 1 that it is not sufficient but could you please explain stmt 2.. As the ad=cf doesnt it mean that they are the diameters

Hi kasturi72,

Any two equal chords of a circle which intersect each other need not be diameters of the circles. They may be just two chords of the circle. The second diagram shown by Bunuel is a good illustration of two equal chords AD and CF intersecting each other at some point M which is not the center of the circle.

Hope it's clear

Regards
Harsh
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Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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28 May 2015, 07:56
Intern
Joined: 28 Dec 2012
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Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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30 May 2015, 07:14
In respect of statement 2, if we were told that M is the center of the circle then would 2 have been sufficient?
Manager
Joined: 06 Mar 2014
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GMAT Date: 04-30-2015
Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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10 Sep 2015, 09:05
Bunuel wrote:
Joy111 wrote:
Attachment:
arc.JPG

Is arc ABC equal in length to arc DEF?

Consider two cases below:
Attachment:
Arcs.png

Case 1: M is the center of the circle --> arc ABC = arc DEF;
Case 2: M is NOT the center of the circle --> arc ABC # arc DEF.
Not sufficient.

So is it safe to say that length of an arc can only be determined if we know the angle subtended at the CENTER. ?
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Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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10 Sep 2015, 09:12
earnit wrote:
Bunuel wrote:
Joy111 wrote:
Attachment:
arc.JPG

Is arc ABC equal in length to arc DEF?

Consider two cases below:
Attachment:
Arcs.png

Case 1: M is the center of the circle --> arc ABC = arc DEF;
Case 2: M is NOT the center of the circle --> arc ABC # arc DEF.
Not sufficient.

So is it safe to say that length of an arc can only be determined if we know the angle subtended at the CENTER. ?

Yes, as the formula is :

Length of the arc = radius of the circle * angle subtended at the center by the same arc

Also note that, angle subtended by an arc at the circumfence = 0.5*angle subtended by the same arc at the center.
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Re: Is arc ABC equal in length to arc DEF?  [#permalink]

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18 Dec 2018, 12:50
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Re: Is arc ABC equal in length to arc DEF?   [#permalink] 18 Dec 2018, 12:50
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