I guess this was discussed in a recent thread.

Arc ABC constitutes 2/3 of the perimeter of the circle

2/3 * 2*pi*r = 24
2*r = 24 * 3 / (2 * pi)
2*r = 11

So, diameter = 11

Thank you jay.

Sorry for asking a basic question..but "Arc ABC constitutes 2/3 of the perimeter of the circle" is applicable to all types of triangle in a circle or just equilateral triangle only?

bump...

Haha, nice way to bump!

Anyway, the equilateral triangle, especially because it is equilateral, makes it easy for us to determine the degree measure of the arc.

For another way to look at it, draw three radii: each extending from the centre to the points A, B, and C. Doing so effectively cuts "the pie" into 3 equal slices. Since you know that a full rotation (i.e. 360°), then you can see that the arc constitutes 2 slices of the pie (i.e. 2/3*360°)

Now you don't actually have to calculate any degrees, but by explaining it this way, I feel that I am illustrating the foundation skills behind degrees and circles. That's how i always reduce my circles anyway!