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# In the figure above, equilateral triangle ABC is inscribed in the

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

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21 Dec 2014, 21:24
Thanks Karishma and Bunnuel ,

I was doing it wrong - This shows difference between theoretical knowledge and practical application.
Lesson learnt hard way
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Re: In the figure above, equilateral triangle ABC is inscribed in the [#permalink]

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15 Apr 2016, 09:41
ulm wrote:
Attachment:
Circle.JPG
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

Since the triangle is an equilateral triangle , we can say

AB = BC = AC ( Property of Equilateral Triangle )

Further the arc lengths AB = BC = AC

We are given AB + BC = 24

Or, 2AB (AB + AB ) = 24

Or, AB = 12

As AB = AC , we can say AC = 12

Thus the total circumference of the circle is 12 + 12 + 12 = 36

Now, 2πr = 36

So, πr = 18

Or, 22/7 r = 18

or, r = 5.72

So, Diameter will be 2r = 2*5.72 => ~ 12

Since this is a question of approximation we choose option (C) 11
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Re: In the figure above, equilateral triangle ABC is inscribed in the [#permalink]

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08 Jun 2017, 15:41
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Attached is a visual that should help.
Attachments

Screen Shot 2017-06-08 at 4.31.56 PM.png [ 225.94 KiB | Viewed 430 times ]

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

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26 Dec 2017, 07:38
Can someone help me out here?

everything makes sense up to C=36.

Since the circumference is 36 and Circumference=D*pi or 2*r*pi.

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

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26 Dec 2017, 07:48
teamryan15 wrote:
Can someone help me out here?

everything makes sense up to C=36.

Since the circumference is 36 and Circumference=D*pi or 2*r*pi.

$$c=\frac{24*3}{2}=36=\pi{d}$$;

$$d=\frac{36}{\pi}\approx{\frac{36}{3.14}}\approx{11.5}$$.
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Re: In the figure above, equilateral triangle ABC is inscribed in the   [#permalink] 26 Dec 2017, 07:48

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