In the figure above, equilateral triangle ABC is inscribed

[BTGmoderatorDC]

In the figure above, 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

OA C

Source: GMAT Prep

[Ian Stewart]

By symmetry, since the triangle is equilateral, the length of each circular arc between two adjacent corners of the triangle must make up 1/3 of the entire circumference of the circle. Since the arc ABC is two of those arcs put together, 24 is 2/3 of the circumference, and 36 is the entire circumference. Since the circumference equals π*d, where d is the diameter, π*d = 36, and d = 36/π, and since π is slightly bigger than 3, d is slightly less than 12, and 11 is the only reasonable answer among the choices.

[Scott@TargetTestPrep]

In the figure above, 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

OA C

Source: GMAT Prep

We are given the length of arc ABC is equal to 24. Since arc AB, BC, and CA each represent 1/3 of the circumference, arc ABC represents 2/3 of the circumference. Thus, we can create the following equation.

2/3(circumference) = 24

2/3(Ï€d) = 24

Ï€d = 24 x 3/2

Ï€d = 36

d = 36/Ï€

d ≈ 11

Answer: C