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Attachment:
temp-3.JPG
temp-3.JPG [ 30.88 KiB | Viewed 7912 times ]

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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The key equation is 2/3 of circumference is covered by an equilateral triangle inscribed in a circle.
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