In the figure above, equilateral triangle ABC is inscribed

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

Given that ∆ABC is an equilateral triangle, arc AB, arc BC and arc CA are equal. We have arc ABC = (arc AB + arc BC + arc CA) – arc CA.

=> arc ABC = 24 = Circumference of the circle – 1/3 of Circumference of the circle = 2/3 of Circumference of the circle

=> Circumference of the circle = 24 * 3/2 = 36

=> 36 = πD, where D = diamater of the circle

=> D = appx. 11.

The correct answer: C

Hope this helps!

-Jay
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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 that 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

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

The equilateral triangle cuts the circle in 3 equal arcs.
Arc ABC travels the length of 2 of those arcs .
So, each arc must have length 12, which means the TOTAL CIRCUMFERENCE = (3)(12) = 36

Now, we'll use the formula: CIRCUMFERENCE = (π)(diameter)
So, 36 ≈ (3.14)(diameter)
This means that: diameter = 36/3.14

IMPORTANT: We need not perform any long division here. Notice that the answer choices are nicely spread apart. So, we can ESTIMATE.
We know that 36/3 = 12
Since 3.14 is a bit bigger than 3, we know that 36/3.14 will be a bit smaller than 12.

Answer choice C is a bit smaller than 12, so it must be the correct answer.

Cheers,
Brent