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In the figure above, equilateral triangle ABC is inscribed

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by BTGmoderatorDC » Fri Aug 16, 2019 5:30 pm

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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

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by Jay@ManhattanReview » Sun Aug 18, 2019 10:12 pm
BTGmoderatorDC wrote:Image

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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by swerve » Mon Aug 19, 2019 9:48 am
Let center be denoted as O. Draw lines OA & OC. Now Angle ABC=60(equilateral triangle) & hence Angle AOC=120.

Length of the arc ABC = (x /360) * circumference, where x = 240 (ext. angle of O)

\(24 = \frac{240}{360}\cdot 2 \pi \cdot r\)
\(D = \frac{36\cdot 7}{22} \approx 11.14 \approx 11 \Rightarrow\) __C__.
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by Scott@TargetTestPrep » Sun Aug 25, 2019 5:30 pm
BTGmoderatorDC wrote:Image

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(Ï€d) = 24

Ï€d = 24 x 3/2

Ï€d = 36

d = 36/Ï€

d ≈ 11

Answer: C

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by Brent@GMATPrepNow » Mon Aug 26, 2019 5:23 am
BTGmoderatorDC wrote:Image

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 = (Ï€)(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
Brent Hanneson - Creator of GMATPrepNow.com
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