The equilateral triangle ABC is inscribed within a circle as

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sat Nov 30, 2019 4:46 am

The equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36Ï€, what is the length of minor arc AC?

A. 3Ï€

B. 4Ï€

C. 5Ï€

D. 6Ï€

E. 9Ï€

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sat Nov 30, 2019 4:46 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Dec 02, 2019 9:27 pm

M7MBA wrote:

The equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36Ï€, what is the length of minor arc AC?

A. 3Ï€

B. 4Ï€

C. 5Ï€

D. 6Ï€

E. 9Ï€

[spoiler]OA=B[/spoiler]

We know that the area of a circle is Ï€r^2 = 36Ï€. Thus, r = radius = 6.

Thus, the circumference of the circle = 2Ï€r = 2Ï€*6 = 12Ï€

Since âˆ†ABC is an equilateral triangle, all the three arcs AB, BC, and CA are equal, thus, the length of minor arc AC = 12Ï€/3 = 4Ï€

The correct answer: B

Hope this helps!

-Jay
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Source: Veritas Prep

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Dec 05, 2019 7:03 pm

M7MBA wrote:

The equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36Ï€, what is the length of minor arc AC?

A. 3Ï€

B. 4Ï€

C. 5Ï€

D. 6Ï€

E. 9Ï€

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

Minor arc AC is 1/3 of the circumference.

Since the area of the circle is 36Ï€, the radius is 6, and thus, the circumference is 12Ï€. Minor arc AC is therefore 1/3 x 12Ï€ = 4Ï€.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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