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# In the figure above, an equilateral triangle is inscribed in a circle

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Math Expert
Joined: 02 Sep 2009
Posts: 56275
In the figure above, an equilateral triangle is inscribed in a circle  [#permalink]

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13 Aug 2018, 04:46
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:49) correct 29% (02:38) wrong based on 40 sessions

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In the figure above, an equilateral triangle is inscribed in a circle. If the arc bounded by adjacent corners of the triangle is between $$4\pi$$ and $$6\pi$$ long, which of the following could be the diameter of the circle?

(A) 6.5
(B) 9
(C) 11.9
(D) 15
(E) 23.5

Attachment:

circle.jpg [ 20.08 KiB | Viewed 763 times ]

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

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13 Aug 2018, 08:48
2
Bunuel wrote:

In the figure above, an equilateral triangle is inscribed in a circle. If the arc bounded by adjacent corners of the triangle is between $$4\pi$$ and $$6\pi$$ long, which of the following could be the diameter of the circle?

(A) 6.5
(B) 9
(C) 11.9
(D) 15
(E) 23.5

Attachment:
circle.jpg

We know that, each of the three arcs corresponds to 120 degree central angle. (Since the measure of central angle is twice the measure of angle at circumference).
hence each arc bounded by adjacent corners of the triangle corresponds to one-third of the circumference of circle.

Given, $$4\pi$$<$$\frac{2\pi*r}{3}$$<$$6\pi$$
Or, 4*3<2r<6*3
Or, 12<d<18

Among the options, 15 is in the range of diameter.

Ans. (D)
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PKN

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Re: In the figure above, an equilateral triangle is inscribed in a circle   [#permalink] 13 Aug 2018, 08:48
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