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An equilateral triangle is inscribed in circle. The length

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chandra23
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An equilateral triangle is inscribed in circle. The length [#permalink] New post   31 Jan 2008, 00:13
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An equilateral triangle is inscribed in circle. The length of the arc is 24, what is the radius of the circle.

I came across the above questions, but do not have answer options. Can someone tell me how to solve above problem?



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Re: An equilateral triangle is inscribed in circle. The length [#permalink] New post   31 Jan 2008, 02:11
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chandra23 wrote:
An equilateral triangle is inscribed in circle. The length of the arc is 24, what is the radius of the circle.

I came across the above questions, but do not have answer options. Can someone tell me how to solve above problem?


2*pi*r = 3*24
r=36/pi
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bhatia_ash2002
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Re: An equilateral triangle is inscribed in circle. The length [#permalink] New post   31 Jan 2008, 08:10
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chandra23 can you please explain?
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hotdog
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Re: An equilateral triangle is inscribed in circle. The length [#permalink] New post   31 Jan 2008, 09:16
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set up an equation:

because it is an eq tri, you know that all angles are equal, thus 24 represents 1/3 of the circ. (using angles 120/360)

so: 1/3=24/circ
circ = 72
solve for d= 72/pi
solve for r=36/pi
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Re: An equilateral triangle is inscribed in circle. The length [#permalink] New post   31 Jan 2008, 14:56
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As long as you know the formula for the circumference of a circle this problem should be very easy

2 * pi * r = circumference

Always use a diagram

Since you have an equilateral triangle within a circle you know that one arc (24) equals 1/3 of the entire circumference

so 2 * pi * r = 3 * 24
2 * pi * r = 72
pi * r = 36
r = 36 / pi
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Re: An equilateral triangle is inscribed in circle. The length [#permalink] New post   31 Jan 2008, 16:36
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chandra23 wrote:
An equilateral triangle is inscribed in circle. The length of the arc is 24, what is the radius of the circle.

I came across the above questions, but do not have answer options. Can someone tell me how to solve above problem?


Which arc? I don't know how you are coming up with answers here. The arc could be 1 side of the traingle or 2 sides.

1 case leaves you a radius of 36/pi, the other 18/pi.



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Re: An equilateral triangle is inscribed in circle. The length [#permalink]
31 Jan 2008, 16:36
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