You do this in two ways.

First method:

arc ABC =24

The triangle is an equilateral triangle the angle b would be 60, therefore the central angle formed at the center of the circle is 120. You can easily find the arc AC => (120/360)*2(pi)r

arc AC+ arc ABC = 2(pi)r


(120/360)*2(pi)r + 24 = 2(pi)r
pi=22/7

If you solve the above equation, r= 5.7
diameter = 2*5.7 = 11.4= 11 approx.

Second Method (easier one):

The triangle is an equilateral triangle therefore every arc would be of same length.

arc AB = 12,
arc BC = 12
arc AC = 12

arc AB+arc BC+arc AC = 36

36=2(pi)r
r=5.7
d=2r=11.4 or 11

Let me know if you still have any doubts.

hey parallel_chase!

i didn't understand how u came up with arc 12 each...though arc abc is given 24.

please help me to figure it out

The equilateral triangle is inscribed in the circle, so there are 3 arcs between the vertex of the triangle: AB, BC, AC. Given the triangle is equilateral they will have the same length.
You know 24=2/3X X=36
And each one is 12

The first method is awesome - agreed a little time consuming .. but gets down to the basics .. I just got the first part that is angle subtended at the center .. and then gave up - because of lack of time.

Thanks for the explanation.