• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Most awarded test prep in the world
Now free for 30 days

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

## Geometry

tagged by: Brent@GMATPrepNow

This topic has 7 expert replies and 5 member replies
RiyaR Senior | Next Rank: 100 Posts
Joined
31 May 2014
Posted:
98 messages
Followed by:
2 members
1

#### Geometry

Sun Oct 05, 2014 3:58 am
A circle with a radius of 4 has an equilateral traingle inscribed in it. What is the perimeter of the inscribed equilateral triangle?

A) 6 root 2
B) 6 root 3
C) 12 root 3
D) 12 root2
E) 24

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9182 messages
Followed by:
472 members
2867
GMAT Score:
800
Tue May 17, 2016 11:03 pm

There are a few specific rules at play in this question that help to make the deductions that come later:

1) The triangle is EQUILATERAL, which means that the 3 sides are the SAME length (and by extension, none of them could be the diameter of the circle - since a diameter is the longest distance between any two points on the circle, you can't make a triangle with three of those lengths).
2) Since the triangle is INSCRIBED, and each of the vertices is the same distance from the center of the circle, that triangle can be 'cut into' three identical ISOSCELES triangles.
3) Those 3 identical isosceles triangles are centered around the center of the circle. Since a circle is 360 degrees, and the triangles are identical, each of those 'central' angles is 120 degrees (and by extension, each of the triangles is a 30/30/120 triangle - and each of THOSE triangles can be cut into two 30/60/90 triangles).

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

prada Senior | Next Rank: 100 Posts
Joined
08 Dec 2010
Posted:
64 messages
1
Tue May 17, 2016 2:37 pm
Hey Guys, maybe there is some concepts I am missing but how did Brent conclude that the angles of the triangle are 120 degrees? From there the vertices would be radii? Is there some rule about inscribed equilateral triangles I don't know? I was trying to imagine the shape of the inscribed triangle in my head and I was thinking hmmmm maybe the base of the triangle could be the diameter of the circle maybe not? thx

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13900 messages
Followed by:
1808 members
13060
GMAT Score:
790
Sun Oct 05, 2014 4:08 am

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11275 messages
Followed by:
1225 members
5254
GMAT Score:
770
Sun Oct 05, 2014 7:39 am
RiyaR wrote:
A circle with a radius of 4 has an equilateral triangle inscribed in it. What is the perimeter of the inscribed equilateral triangle?

A) 6âˆš2
B) 6âˆš3
C) 12âˆš3
D) 12âˆš2
E) 24
So, here's what the diagram looks like.

If we draw lines from the center to each vertex, we get the following:

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 60Âº angle must have length 2âˆš3

This means ONE side of the equilateral triangle has length 4âˆš3, so the PERIMETER = 4âˆš3 + 4âˆš3 + 4âˆš3 = 12âˆš3

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9182 messages
Followed by:
472 members
2867
GMAT Score:
800
Sun Oct 05, 2014 10:15 am
Hi RiyaR,

The answer choices to this question are written in such a way so that you can logically get to the correct answer and avoid most of the math. Here's why:

We're told that the radius of the circle = 4, so the diameter = 8.

An equilateral triangle inscribed into a circle will have 3 equal sides that are each GREATER than the radius but LESS than the diameter. We're asked to figure out the perimeter of the triangle.

3(radius) = 12 --> too small
3(diameter) = 24 --> too big

With this, we can eliminate A and B (too small) and E (too big)

With the remaining two answers (12root3 and 12root2), we have to think about which root we're likely to be dealing with. An equilateral triangle has three 60 degree angles in it, so we should be able to break this triangle into smaller triangles (probably a bunch of 30/60/90 triangles - which include a root3 in the "math" for figuring out some of the side lengths). It stands to reason that root3 would be part of the final calculation.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

Jacob003 Senior | Next Rank: 100 Posts
Joined
22 Sep 2014
Posted:
38 messages
1
Tue Oct 07, 2014 9:50 am
Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?
you can check for more questions here http://questionbank.4gmat.com/mba_prep_sample_questions/geometry/

bakhtawer Newbie | Next Rank: 10 Posts
Joined
29 Dec 2015
Posted:
1 messages
Tue Dec 29, 2015 2:37 am
Hi I can't seem to find videos for Coordinate geometry in the geometry module.Could anyone guide me >

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11275 messages
Followed by:
1225 members
5254
GMAT Score:
770
Tue Dec 29, 2015 5:49 am
IMO, coordinate geometry is more about solutions to equations than it is to geometry.
We (GMAT Prep Now) place it in our Algebra & Equation-Solving module (http://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving)

See videos #43 to #54

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

Last edited by Brent@GMATPrepNow on Tue May 17, 2016 3:54 pm; edited 1 time in total

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9182 messages
Followed by:
472 members
2867
GMAT Score:
800
Tue Dec 29, 2015 10:09 pm
Hi bakhtawer,

You've mentioned that you can't find certain videos in the materials that you're using - but what resources are you currently using to study for the GMAT?

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

prada Senior | Next Rank: 100 Posts
Joined
08 Dec 2010
Posted:
64 messages
1
Wed May 18, 2016 7:04 am
Rich.C@EMPOWERgmat.com wrote:

There are a few specific rules at play in this question that help to make the deductions that come later:

1) The triangle is EQUILATERAL, which means that the 3 sides are the SAME length (and by extension, none of them could be the diameter of the circle - since a diameter is the longest distance between any two points on the circle, you can't make a triangle with three of those lengths).
2) Since the triangle is INSCRIBED, and each of the vertices is the same distance from the center of the circle, that triangle can be 'cut into' three identical ISOSCELES triangles.
3) Those 3 identical isosceles triangles are centered around the center of the circle. Since a circle is 360 degrees, and the triangles are identical, each of those 'central' angles is 120 degrees (and by extension, each of the triangles is a 30/30/120 triangle - and each of THOSE triangles can be cut into two 30/60/90 triangles).

GMAT assassins aren't born, they're made,
Rich
Cool, thanks Rich. I dont recall ever seeing that info in Magoosh or MGMAT study guides. Of course that can be deduced by knowing the "elementary" rules and properties. These are things I need to study and think about more. thx

Gurpreet singh Senior | Next Rank: 100 Posts
Joined
28 Apr 2016
Posted:
38 messages
1
Tue Jun 07, 2016 6:42 am
Formula for radius of an inscribed equilateral triangle =a/root3

ie r=a/root3

r=4
a=side of the traingle

ie
4=a/root3=4root3=a multiply both the sides by 3(perimeter of a traingle is sum of 3 sides)

ans-12root3[/spoiler][/list]

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
625
Target GMAT Score:
V51
GMAT Score:
780
Tue Jun 07, 2016 11:07 pm
Brent@GMATPrepNow wrote:
IMO, coordinate geometry is more about solutions to equations than it is to geometry.
Totally agree!

Also think that geometry seems to be dying on the GMAT: there is so much less of it these days, particularly the more elaborate questions. That can always change, but the more arcane (by GMAT standards) geometric properties seem less relevant than ever.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### Best Conversation Starters

1 lheiannie07 112 topics
2 ardz24 71 topics
3 Roland2rule 69 topics
4 LUANDATO 53 topics
5 swerve 45 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

154 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

107 posts
3 Jeff@TargetTestPrep

Target Test Prep

106 posts
4 Scott@TargetTestPrep

Target Test Prep

98 posts
5 EconomistGMATTutor

The Economist GMAT Tutor

91 posts
See More Top Beat The GMAT Experts