GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
What is the perimeter of an equilateral triangle inscribed in a circle
[#permalink]
04 Jun 2021, 10:28
04 Jun 2021, 10:28
Expert Reply
1
Bookmarks
00:00
Question Stats:
61% (01:30) correct
38% (01:55) wrong based on 26 sessions
Hide Show timer Statistics
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?
A. \(6\sqrt{2}\)
B. \(6\sqrt{3}\)
C. \(12\sqrt{2}\)
D. \(12\sqrt{3}\)
E. \(24\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(6\sqrt{2}\)
B. \(6\sqrt{3}\)
C. \(12\sqrt{2}\)
D. \(12\sqrt{3}\)
E. \(24\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the perimeter of an equilateral triangle inscribed in a circle
[#permalink]
04 Jun 2021, 10:41
04 Jun 2021, 10:41
1
Carcass wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?
A. \(6\sqrt{2}\)
B. \(6\sqrt{3}\)
C. \(12\sqrt{2}\)
D. \(12\sqrt{3}\)
E. \(24\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(6\sqrt{2}\)
B. \(6\sqrt{3}\)
C. \(12\sqrt{2}\)
D. \(12\sqrt{3}\)
E. \(24\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
So, here's what the diagram looks like.
If we draw lines from the center to each vertex, we get the following:
Since the radii have length 4, we can add that here:
Now we'll draw a line from the center that is PERPENDICULAR to one side of the tirangle.
We now have a SPECIAL 30-60-90 right triangle.
Here's the base version of this SPECIAL TRIANGLE
We can see that the each 30-60-90 triangle in the diagram is TWICE as big as the base version. So, each side opposite the 60º angle must have length 2√3
This means ONE side of the equilateral triangle has length 4√3, so the PERIMETER = 4√3 + 4√3 + 4√3 = 12√3
Answer: C
Cheers,
Brent
gmatclubot
Re: What is the perimeter of an equilateral triangle inscribed in a circle [#permalink]
04 Jun 2021, 10:41
Moderators:
