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# In the figure above, equilateral triangle ABC is inscribed

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Director
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In the figure above, equilateral triangle ABC is inscribed [#permalink]  20 Aug 2005, 14:44
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Question Stats:

67% (01:48) correct 33% (01:01) wrong based on 362 sessions

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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SVP
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Re: PS-Geometry [#permalink]  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]  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...
Director
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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
Director
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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink]  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

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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink]  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

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 $$c=\frac{24*3}{2}=36=\pi{d}$$ --> $$d\approx{11.5}$$.

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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