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

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In the figure above, an equilateral triangle is inscribed in [#permalink]  12 Aug 2018, 10:12
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#GREpracticequestion In the figure above, an equilateral triangle is.jpg [ 20.08 KiB | Viewed 826 times ]

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
[Reveal] Spoiler: OA

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Re: In the figure above, an equilateral triangle is inscribed in [#permalink]  18 Aug 2018, 20:09
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Carcass wrote:
Attachment:
circle.jpg

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

Here we need to consider the both the arc length i.e. $$4\pi$$ and $$6\pi$$

Since all the angles of equilateral triangle = 60°

Therefore
$$\frac{{central angle}}{360}= \frac{{Arc length}}{circumference}$$

$$\frac{120}{360}= \frac{{4\pi}}{{2\pi*radius}}$$

or $$radius = 6$$

or $$diameter = 12$$

Now if we consider arc length as $$6\pi$$ then,

$$\frac{{central angle}}{360} = \frac{{6\pi}}{{2\pi*radius}}$$

$$\frac{120}{360}= \frac{{6\pi}}{{2\pi*radius}}$$

or $$radius = 9$$

or $$diameter = 18$$

So only Option D satisfy
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Re: In the figure above, an equilateral triangle is inscribed in [#permalink]  01 Feb 2019, 17:35
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Expert's post
Carcass wrote:
Attachment:
circle.jpg

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

Since each arc is bounded by adjacent corners of the triangle representing 1/3 of the circumference, the range of values of the circumference is:

Minimum:

1/3(C) = 4π

C = 12π, so the diameter would be 12.

Maximum:

1/3(C) = 6π

C = 18π, so the diameter would be 18.

The diameter is between 12 and 18, so a possible diameter is 15.

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Re: In the figure above, an equilateral triangle is inscribed in   [#permalink] 01 Feb 2019, 17:35
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