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# The length of minor arc AB is twice the length of minor arc

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Manager
Joined: 03 Jul 2007
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The length of minor arc AB is twice the length of minor arc [#permalink]  17 Dec 2007, 12:48
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

A, 20
B, 40
C, 60
D, 80
E, 120

I have no idea on where to begin. Please see below for the diagram. Thanks!!
Attachments

File comment: Circle

circle.GIF [ 3.82 KiB | Viewed 758 times ]

CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 399

Kudos [?]: 2092 [0], given: 359

Expert's post
I guess B. I just will try to draw...

....I've finished.

From question: AB=2BC and AC=3AB

1. Let x=BC, So, AB=2x and AC=6x.

2. Now, we can find angles for our minor arcs: 6x+2x+x=360 ==> x=40

3. angle AOC = 40+80=120. angle OAC=angle OCA=(180-120)/2=30

4. angle OCB=angle OBC=(180-40)/2=70

5. angle BCA= angle BCO - angle ACO=70-30=40
Attachments

t57215.gif [ 11.41 KiB | Viewed 747 times ]

Intern
Joined: 13 Jun 2007
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There is a mistake in the question.

Quote:
length of minor arc AC is three times the length of minor arc AB

Since AC = 6x
AB=2x and
BC=x
Then 6x should be the MAJOR arc of AC and not the minor.
because the minor is equal to 3x

Walker's answer is correct as usual
Director
Joined: 08 Jun 2007
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Re: Triangle and circle [#permalink]  17 Dec 2007, 16:09
pinal2 wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

A, 20
B, 40
C, 60
D, 80
E, 120

I have no idea on where to begin. Please see below for the diagram. Thanks!!

I guess the diagram in the question misleading. I am not sure if this was really attached with the question.
But any way the angles are in ratio 6:3:1 , and from that we can figure out the way Walker proceeded.
Intern
Joined: 13 Jun 2007
Posts: 48
Followers: 1

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The diagram is correct.
I believe the question has an error in it
CEO
Joined: 29 Mar 2007
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walker wrote:
I guess B. I just will try to draw...

....I've finished.

From question: AB=2BC and AC=3AB

1. Let x=BC, So, AB=2x and AC=6x.

2. Now, we can find angles for our minor arcs: 6x+2x+x=360 ==> x=40

3. angle AOC = 40+80=120. angle OAC=angle OCA=(180-120)/2=30

4. angle OCB=angle OBC=(180-40)/2=70

5. angle BCA= angle BCO - angle ACO=70-30=40

Same approach, but its not very hard to do. I just did it in my head. We have x+2x+6x=9x=180 x=20 We are looking for BCA or essentially AB

so 2*20=40.

Walker what program are you using to make those diagrams? is it possible that you could send it to me?
Manager
Joined: 03 Jul 2007
Posts: 53
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Kudos [?]: 0 [0], given: 0

I pasted the question and the diagram from MGMAT.

OA is indeed B, 40.

Great explanation guys.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 399

Kudos [?]: 2092 [0], given: 359

Expert's post
GMATBLACKBELT wrote:
Same approach, but its not very hard to do. I just did it in my head. We have x+2x+6x=9x=180 x=20 We are looking for BCA or essentially AB

so 2*20=40.

GMATBLACKBELT wrote:
Walker what program are you using to make those diagrams? is it possible that you could send it to me?

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