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In the figure above, equilateral triangle ABC is inscribed

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In the figure above, equilateral triangle ABC is inscribed

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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

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BTGmoderatorDC wrote:


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(πd) = 24

πd = 24 x 3/2

πd = 36

d = 36/π

d ≈ 11

Answer: C

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Founder and CEO
scott@targettestprep.com



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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.

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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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