Since the Arc made by two adjacent corners of the triangle is making 120˚ angle at the center so length of the arc is given by \(\frac{120˚}{360˚} *2 \pi r\)
[ Watch this video to know how ]

=> Arc length = \(\frac{1}{3} *2 \pi r\) and it is between \(4\pi\) and \(6\pi\)

=> \(4\pi\) <\(\frac{1}{3} *2 \pi r\) < \(6\pi\)
=> 4 < \(\frac{d}{3}\) < 6 (as Diameter (d) = 2r)
=> 4*3 < d < 3*6
=> 12 < d < 18

Only Option D (15) is in this range

So, Answer will be D
Hope it helps!

Watch the following video to Learn Properties of Equilateral Triangle inscribed in a Circle


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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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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.

Answer: D
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Arc bounded by adjacent corners of an Equilateral triangle in a circle would be 120 degrees (360/3)
So, it's length would be (1/3)rd the Circumference of circle.

4π < C/3 < 6π
12π < C < 18π

Since, C = 2πr = πd
Therefore,

12 < d < 18

Hence, option D
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