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Is arc ABC equal in length to arc DEF?

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Is arc ABC equal in length to arc DEF? [#permalink]

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New post 31 May 2012, 04:26
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Question Stats:

30% (00:40) correct 70% (00:39) wrong based on 222 sessions

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Attachment:
arc.JPG
arc.JPG [ 6.11 KiB | Viewed 5346 times ]


Is arc ABC equal in length to arc DEF?

(1) AD⊥CF
(2) AD=CF
[Reveal] Spoiler: OA

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

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New post 31 May 2012, 04:49
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Joy111 wrote:
Attachment:
The attachment arc.JPG is no longer available


Is arc ABC equal in length to arc DEF?

(1) AD⊥CF
(2) AD=CF


Consider two cases below:
Attachment:
Arcs.png
Arcs.png [ 13.11 KiB | Viewed 5292 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.

Answer: E.
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Is arc ABC equal in length to arc DEF? [#permalink]

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New post 27 May 2015, 22:10
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

Last edited by kasturi72 on 28 May 2015, 06:56, edited 1 time in total.

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

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New post 28 May 2015, 02:18
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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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New post 28 May 2015, 06:56
Thanks harsh that was helpful

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

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New post 30 May 2015, 06:14
In respect of statement 2, if we were told that M is the center of the circle then would 2 have been sufficient?

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

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New post 10 Sep 2015, 08:05
Bunuel wrote:
Joy111 wrote:
Attachment:
arc.JPG


Is arc ABC equal in length to arc DEF?

(1) AD⊥CF
(2) AD=CF


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.

Answer: E.


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

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New post 10 Sep 2015, 08:12
earnit wrote:
Bunuel wrote:
Joy111 wrote:
Attachment:
arc.JPG


Is arc ABC equal in length to arc DEF?

(1) AD⊥CF
(2) AD=CF


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.

Answer: E.


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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Re: Is arc ABC equal in length to arc DEF?   [#permalink] 21 Nov 2017, 07:46
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