Hi In this question what is the angle being intercepted?

Equilateral triangle ABC is inscribed in a 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 Figures in PS problems are generally DRAWN TO SCALE. It should be clear from the figure that arc AB = arc BC = arc AC. Thus, arc ABC -- which has a length of 24 -- constitutes 2/3 of the circumference: 24 = (2/3)c c = 36. Since c = πd ≈ 3d, we get: 3d ≈ 36 d ≈ 12. The correct answer is C.

GMATGuruNY wrote: Figures in PS problems are generally DRAWN TO SCALE. It should be clear from the figure that arc AB = arc BC = arc AC. Thus, arc ABC -- which has a length of 24 -- constitutes 2/3 of the circumference: 24 = (2/3)c c = 36. Since c = πd ≈ 3d, we get: 3d ≈ 36 d ≈ 12. The correct answer is C. Hi Mitch, Is the below one correct ? The radius of the circumscribed circle is R= (SQRT(3)/3) *a The radius of the inscribed circle is r= (SQRT(3)/6)*a, where a is the side of the equilateral triangle. If it is, then from the question we know a = 8 then R = SQRT(3)/3 *8 so diameter is 9.23 so closest ans is 8. so we should pick B only right instead of C Could you please explain this. Thanks in advance. Regards, Uva.

The radius of the inscribed circle is r= (SQRT(3)/6)*a, where a is the side of the equilateral triangle. from the question we know a = 8 The question stem indicates that arc ABC = 24. This does not imply that each side of the triangle has a length of 8.

GMATGuruNY wrote:Uva@90 wrote:a is the side of the equilateral triangle.[/color] from the question we know a = 8 The question stem does not indicate that a=8. The shortest distance between two points is a straight line. Thus, an arc that connects points A and B must be longer than a straight line that connects points A and B. Since arc AB = 8, line segment AB must be LESS than 8. Thus, a<8. OMG!! I Completely misunderstood the question. Question states LENGTH OF ARC =24. I understood as length of line segment =24 i.e sum of each sides of triangle =24. Thanks a ton Mitch. Regards, Uva.