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In the figure above, equilateral triangle ABC is inscribed

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In the figure above, equilateral triangle ABC is inscribed [#permalink] New post 20 Aug 2005, 14:44
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In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

A. 5
B. 8
C. 11
D. 15
E. 19

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-above-equilateral-triangle-abc-is-inscribed-97393.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Jul 2013, 02:29, edited 1 time in total.
Edited the question and added the OA.
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Re: PS-Geometry [#permalink] New post 20 Aug 2005, 18:20
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C = 2 (pi) r = 24/2x3=36
(pi) d = 36
d = 36x7/22=126/11=11
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Re: PS-Geometry [#permalink] New post 20 Aug 2005, 22:29
ALI1 wrote:
HIMALAYA wrote:
C = 2 (pi) r = 24/2x3=36
(pi) d = 36
d = 36x7/22=126/11=11
Himalaya can u plz explain


since, the triangle is equilateral. so, ab=bc=ca
arc abc=24,
arc abc covers 2/3 of the whole perimeter.
so, the the whole perimeter (2 pi r) = 24/(2/3) = 36
2r=d=36/pi=11 approx...
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 [#permalink] New post 21 Aug 2005, 09:14
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Or you can say that each side of the triangle covers 120 degrees.

length of acc conered by 2 sides is = 24

meaning 240 degrees conver 24

360 will cover 36 units

pi*d = 36

d = 11 approx
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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink] New post 22 Jul 2013, 01:23
In the triangle the corresponding angles are 60 degrees so the arc will be 120 and 120

total would be 240

Length of arch 240/360 * 2 Pi r = 24 >> r is approx 6

diameter is 12

not there in answer choices closest answer is 11
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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink] New post 22 Jul 2013, 02:30
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fozzzy wrote:
In the triangle the corresponding angles are 60 degrees so the arc will be 120 and 120

total would be 240

Length of arch 240/360 * 2 Pi r = 24 >> r is approx 6

diameter is 12

not there in answer choices closest answer is 11


Image
In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

A. 5
B. 8
C. 11
D. 15
E. 19

Arc ABC is \frac{2}{3} of the circumference (as ABC is equilateral triangle and thus arc AB=arc BC=arc AC, so arc AB+arc BC=arc ABC = 2/3 of circumference) --> 24=c*\frac{2}{3}, hence circumference c=\frac{24*3}{2}=36=\pi{d} --> d\approx{11.5}.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-above-equilateral-triangle-abc-is-inscribed-97393.html
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Re: In the figure above, equilateral triangle ABC is inscribed   [#permalink] 22 Jul 2013, 02:30
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In the figure above, equilateral triangle ABC is inscribed

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