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arclength of circle with equilateral triangle

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asadullah100
 Post subject: arclength of circle with equilateral triangle
 Post Posted: Fri Nov 06, 2009 10:11 am 
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Students


Posts: 2
kindly help me out in solving this problem.. your response will be highly appreciated... what will be the angle for this in arclength formula.... the correct answer was 11 in gmat prep... thanks...


Q: what is the approximate diameter of a circle with an equilateral triangle ABC inside it having arclength ABC equal to 24?
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lalitkc
 Post subject: Re: arclength of circle with equilateral triangle
 Post Posted: Sat Nov 07, 2009 12:55 am 
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Students


Posts: 11
Q: what is the approximate diameter of a circle with an equilateral triangle ABC inside it having arclength ABC equal to 24?

Let O be the centre of the circle.
In equilateral triangle ABC,
<ABC = 60 ,
<AOC = 2 <ABC = 120 .....property : central angle = 2 * inscribed angle
l (arc) / circumference = central angle / 360
l (arc AC) = 12
120/360 = 12/ (Pi * d)
d= 11.45
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geetesht
 Post subject: Re: arclength of circle with equilateral triangle
 Post Posted: Sun Nov 15, 2009 1:31 pm 
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Course Students


Posts: 16
lalitkc wrote:
Q: what is the approximate diameter of a circle with an equilateral triangle ABC inside it having arclength ABC equal to 24?

Let O be the centre of the circle.
In equilateral triangle ABC,
<ABC = 60 ,
<AOC = 2 <ABC = 120 .....property : central angle = 2 * inscribed angle
l (arc) / circumference = central angle / 360
l (arc AC) = 12
120/360 = 12/ (Pi * d)
d= 11.45


lalit,

how about we juz use this formula after having derived the central angel as 120

(240/360 ) * 2 pi radius = 24 (Length of arc ABC)

OR

(2/3) * pi Diameter = 24

OR

Diameter = (24 * 3)/(2 pi)

Diameter = 11.45
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RonPurewal
 Post subject: Re: arclength of circle with equilateral triangle
 Post Posted: Fri Dec 18, 2009 5:47 am 
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ManhattanGMAT Staff


Posts: 7146
co-ordinate-gprep-t2660.html

please search the forum!

not only will this help us avoid multiple posts on the same problem, but you'll get feedback instantly instead of having to wait.
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