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# In the figure above, equilateral triangle ABC is inscribed

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

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21 Dec 2014, 21:56
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Expert's post
him1985 wrote:

I still can not understand how it becomes 240+240 . I have attached the figure.
Can you please clear my doubt.

Let me add to what Bunuel said by giving you a figure (excuse my drawing) that will help you determine central angles.

Attachment:

Ques3.jpg [ 15.73 KiB | Viewed 1059 times ]

The red arc subtends the red central angle. It is the angle formed by the red lines at the center (toward the red arc)
The green arc subtends the green angle at the center formed by green lines (toward the arc).
So the blue arc will also subtend the blue angle formed by blue lines (toward the arc). This angle will be greater than 180 and will be the central angle subtended by the blue arc which is greater than semi circle.
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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink]

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21 Dec 2014, 22:24
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 [#permalink]

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15 Apr 2016, 05:09
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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink]

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15 Apr 2016, 10:41
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 [#permalink]

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16 Apr 2017, 09:24
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Re: In the figure above, equilateral triangle ABC is inscribed [#permalink]

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08 Jun 2017, 16:41
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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 113 times ]

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Re: In the figure above, equilateral triangle ABC is inscribed   [#permalink] 08 Jun 2017, 16:41

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