Question:

Imagine a equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

(a) 5
(b) 8
(c) 11
(d) 15
(e) 19

Answer C

When I solve this question, I am getting 22 as diameter, and 11 as the radius. Can someone please help me if you get the 11 as the answer for the diameter?

This is how I am getting 22.

Since inscribed angle for the triangle is 60, the arc angle will be 120. therefore 24=(120/360)*2pi(r)
36=pi(r)
(r) = 11.
Thus, diameter = 22

Let me know what I am doing wrong.. This question is from the GMAT PREP CD and thus I do not think the CD is wrong.....

thanks

SB

Please read (and follow!) the guidelines in the stickies. GMATPrep problems have their own folders. Also, your subject line should be the first 5-8 words of the problem itself. I'll move this over to the right folder for you this time but please remember for next time! Thanks. :)

I think the solution may be:

Arc Length ABC, if you draw it correctly inscribed in a circle, represents 2/3 of the circle's circumference, not 1/3. So there are two minor arcs measuring 120 degrees, 120/360 + 120/360 = 1/3 +1/3 = 2/3 of 2piR.

Now solving for the approx. value for the Diameter:

24 = 2/3 2piR
divide both sides by 2/3:
36=2piR
divide both sides by pi
36/3.14 = 2R = diameter

Diameter is approx. 11

Hope this helps =p