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