GMAT PREP I #12

[pkw209]

Hi all,

Couldn't figure this one out. Would appreciate a brief explanation. thanks!

Diagram-Try and picture a circle with an equilateral triangle inscribed within it (all three points a, b, and c touching the edge of the circle). just want to make sure it's clear

Q) In the figure, equilateral triangle ABC is inscribed in the circle. If the length of the arc ABC is 24, what is the approximate diameter of the circle?

1) 5

2) 8

3) 11

4) 15

5) 19

[papgust]

I'm not sure whether i'm correctly diagramming it with the given info. In the diagram, I've ignored the arc AC as the length is given only for arc ABC [---Please correct me here if i'm wrong---]

Each angle of the triangle is 60 degrees. So the angle subtended on the arc is 120 degrees [Because the angle at the centre subtended by the arc is 120 (2*60)]. So we have AB as 120 and BC as 120. Totally, 240 degrees.

Now, find the radius of the circle using the formula
Length of arc = Angle of sector/360 * 2 * pi * r

We know that length of arc ABC is 24 and arc ABC is 240 degrees.

24 = 240/360 * 2 * pi * r
r = 18 / pi

Therefore, diameter of a circle = 2 * 18/pi = 11 (Approximately)

Choice C.

[thephoenix]

IMO C

equilateral triangle inscribed in circle will break the circle in three equal arc length

since arc length of ABC is 24 , therefore each arc is 12 and cicumference of circle is 36

now 2 pi r=36
---> d=2r=126/11=approx 11

[pkw209]

you guys are both correct! the answer is c. thank you!

Careless errors always hurt me