GMAT PREP - Easy But not able to do....Pls Help

Chaitanya_1986 wrote:Pls help

The most useful thing is to see that the triangle has equal angles. Therefore, arc AB = arc BC = arc AC. So let's represent arc AB by X. It follows that the circumference of the circle is X + X + X =3X

But we are given that arc ABC, that is equal to arc AB + arc BC = 24
= 2X = 24
=X = 12.

Hence, the circumference of the circle is 3 *12 = 36 = 2 pi. r
So you shall get r= 36 * (7/22). This is approximately 11.

You could also use the rule that the arc length is the same portion of the circumference as the arc angle is to 360* and the rule that the angle formed when two points are drawn to the edge of the circle is 1/2 the angle when the same two points are drawn to the center of the circle. Therefore you know that the arc that is not calculated is 120* (two times 60*) and therefore the arc represents 240* of the circle.

if 240/360 = 24/circumf. then the circumference is 36.

Circumference can be represented by pi(d)

So if pi(d)=36 then d = 36/pi (you can normally estimate pi to be 3 and you would get 12 - however we know our answer is a little less than 12 because pi is actually bigger than three) therefore your best answer would be 11.