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# Triangle inscribed in Circle Arc Length

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Intern
Joined: 12 Feb 2009
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Triangle inscribed in Circle Arc Length [#permalink]

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27 May 2009, 10:05
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I'm having trouble with this problem. The way I read it the arc in question is 24. Therefore 24=1/3*d*Pi (1/3 since equilateral triangle, so each arc should represent 1/3 of circumference).
(24*3)/PI ~ 23 but this is not the right answer. I was hoping someone could tell me where I am going wrong. Thanks.

Kudos [?]: 11 [0], given: 0

Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
Posts: 209

Kudos [?]: 74 [0], given: 3

Schools: Harvard, Penn, Maryland
Re: Triangle inscribed in Circle Arc Length [#permalink]

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27 May 2009, 13:58
Arc ABC is from point A to C passing through B.

It would equate to 2/3 of the circle, so if arcABC = 24, then the circumference of the circle is 36.

Circumference = pi*diameter

so the equation is

36 = pi * x

so x = 36/pi

11.4 to 11.5 not sure, no calculators lol

Kudos [?]: 74 [0], given: 3

Intern
Joined: 12 Feb 2009
Posts: 26

Kudos [?]: 11 [0], given: 0

Re: Triangle inscribed in Circle Arc Length [#permalink]

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27 May 2009, 14:17
Sorry I don't understand how you are arriving at 2/3. Since it's an equilateral triangle shouldn't the arc formed with each point A, B, and C be equal?

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Manager
Joined: 16 Apr 2009
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Schools: Ross
Re: Triangle inscribed in Circle Arc Length [#permalink]

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27 May 2009, 14:18
Quote:

I'm having trouble with this problem. The way I read it the arc in question is 24. Therefore 24=1/3*d*Pi (1/3 since equilateral triangle, so each arc should represent 1/3 of circumference).
(24*3)/PI ~ 23 but this is not the right answer. I was hoping someone could tell me where I am going wrong. Thanks.

Angle=90*L/pi* r
where L is the length of the arc

60=90*24/pi*r

2=3*24/pi*r

pi*r=12*3
r=36/3.14

therefore r=11.47
_________________

Keep trying no matter how hard it seems, it will get easier.

Kudos [?]: 101 [0], given: 10

Intern
Joined: 12 Feb 2009
Posts: 26

Kudos [?]: 11 [0], given: 0

Re: Triangle inscribed in Circle Arc Length [#permalink]

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27 May 2009, 14:26
Ok I see now. The arc is actually defined by the points ABC on the circle (which is 2/3 of the circle) I was reading it incorrectly. Thanks!

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Re: Triangle inscribed in Circle Arc Length   [#permalink] 27 May 2009, 14:26
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