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# An equilateral triangle ABC is inscribed in the circle. If

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Senior Manager
Joined: 24 Mar 2011
Posts: 356
Location: Texas
An equilateral triangle ABC is inscribed in the circle. If  [#permalink]

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23 Apr 2011, 14:32
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00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:56) correct 35% (02:01) wrong based on 159 sessions

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An equilateral triangle ABC is inscribed in the circle. If the length of the 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: http://gmatclub.com/forum/in-the-figure ... 97393.html
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Joined: 14 Feb 2011
Posts: 175
Re: An equilateral triangle ABC is inscribed in the circle. If  [#permalink]

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23 Apr 2011, 15:42
Since ABC is an equilateral triangle, arc ABC is 2/3 of circumference, so circumference equals 24*3/2 = 36

$$\pi * Diameter = 36$$ , so Diameter ~11
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Re: An equilateral triangle ABC is inscribed in the circle. If  [#permalink]

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24 Apr 2011, 20:50
24/pi*D = 240/360 (Angle subtended by arc ABC = 240)

=> D = 36/pi = 36/3.14 ~ 11

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Re: An equilateral triangle ABC is inscribed in the circle. If  [#permalink]

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01 Oct 2016, 20:05
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1
agdimple333 wrote:
An equilateral triangle ABC is inscribed in the circle. If the length of the arc ABC is 24, what is the approximate diameter of the circle.

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

Ans C ..plz follow as attached below
Attachments

eq.png [ 15.87 KiB | Viewed 1195 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: An equilateral triangle ABC is inscribed in the circle. If  [#permalink]

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14 Jan 2018, 05:40

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: http://gmatclub.com/forum/in-the-figure ... 97393.html
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Re: An equilateral triangle ABC is inscribed in the circle. If &nbs [#permalink] 14 Jan 2018, 05:40
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