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# Triangle inscribed in Circle Arc Length

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Triangle inscribed in Circle Arc Length [#permalink]  27 May 2009, 09:05
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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.
Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
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Schools: Harvard, Penn, Maryland
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Re: Triangle inscribed in Circle Arc Length [#permalink]  27 May 2009, 12:58
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
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Re: Triangle inscribed in Circle Arc Length [#permalink]  27 May 2009, 13:17
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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Re: Triangle inscribed in Circle Arc Length [#permalink]  27 May 2009, 13:18
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
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Re: Triangle inscribed in Circle Arc Length [#permalink]  27 May 2009, 13:26
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!
Re: Triangle inscribed in Circle Arc Length   [#permalink] 27 May 2009, 13:26
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# Triangle inscribed in Circle Arc Length

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