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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