GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Feb 2019, 17:43

### GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free GMAT Strategy Webinar

February 16, 2019

February 16, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# An equilateral triangle that has an area of 16√ 3 is inscribed in a ci

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52902
An equilateral triangle that has an area of 16√ 3 is inscribed in a ci  [#permalink]

### Show Tags

04 Oct 2018, 23:46
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

69% (02:06) correct 31% (02:10) wrong based on 37 sessions

### HideShow timer Statistics

An equilateral triangle that has an area of 16√3 is inscribed in a circle. What is the area of the circle?

(A) 3π

(B) 16π/3

(C) 64π/3

(D) 12√3*π

(E) 20√3*π

_________________
Senior Manager
Joined: 17 Jan 2017
Posts: 300
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: An equilateral triangle that has an area of 16√ 3 is inscribed in a ci  [#permalink]

### Show Tags

05 Oct 2018, 00:38
1
Bunuel wrote:
An equilateral triangle that has an area of 16√3 is inscribed in a circle. What is the area of the circle?

(A) 3π

(B) 16π/3

(C) 64π/3

(D) 12√3*π

(E) 20√3*π

Area of equilateral triangle = $$16√3 = √3/4 a^2$$
Reducing, $$a = 8$$

Radius of Inscribed circle in a equilateral triangle,$$r = √3/6 a$$
$$r = 4/√3$$

Area of circle,$$A = πr^2$$
$$A = π*16/3$$

+1 for B
_________________

Only those who risk going too far, can possibly find out how far one can go

Intern
Joined: 10 Dec 2017
Posts: 24
Location: India
An equilateral triangle that has an area of 16√ 3 is inscribed in a ci  [#permalink]

### Show Tags

Updated on: 05 Oct 2018, 02:19
1
Area of an equilateral triangle is = √3/4a2 = 16√3
this gives a=8
We also know that half of an equilateral triangle is a 30-60-90 triangle with the longest side 'a', and sides of this triangle are in the ratio of x:x√3: 2x.
so a=2x
X=a/2
Hence, x√3=√3a/2 this is nothing but the median(altitude) of an equilateral triangle.
The important thing to remember is that the altitude will also be the median and will pass through the center of the circle (since it is an equilateral triangle). We know that centroid divides the median in the ratio 2:1. The centroid will be the center of the circle as each median will pass through it due to the symmetry.
the radius of the circle will be 2/3( median)= 2/3* √3a/2=√3a/3
a=8,this gives us radius= 8*√3/3
Area= πr2=π∗64/3
C:)

Originally posted by satya2029 on 05 Oct 2018, 01:56.
Last edited by satya2029 on 05 Oct 2018, 02:19, edited 1 time in total.
Intern
Joined: 29 Jan 2017
Posts: 6
Re: An equilateral triangle that has an area of 16√ 3 is inscribed in a ci  [#permalink]

### Show Tags

05 Oct 2018, 02:10
1
Akash720 wrote:
Bunuel wrote:
An equilateral triangle that has an area of 16√3 is inscribed in a circle. What is the area of the circle?

(A) 3π

(B) 16π/3

(C) 64π/3

(D) 12√3*π

(E) 20√3*π

Area of equilateral triangle = $$16√3 = √3/4 a^2$$
Reducing, $$a = 8$$

Radius of Inscribed circle in a equilateral triangle,$$r = √3/6 a$$
$$r = 4/√3$$

Area of circle,$$A = πr^2$$
$$A = π*16/3$$

+1 for B

Its the triangle that is inscribed in the circle and not vice versa.
The answer is C.
Director
Joined: 06 Jan 2015
Posts: 586
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: An equilateral triangle that has an area of 16√ 3 is inscribed in a ci  [#permalink]

### Show Tags

05 Oct 2018, 18:49
Bunuel wrote:
An equilateral triangle that has an area of 16√3 is inscribed in a circle. What is the area of the circle?

(A) 3π

(B) 16π/3

(C) 64π/3

(D) 12√3*π

(E) 20√3*π

ABC equatorial triangle inscribed in the circle with radius r is $$(3\sqrt{3}/4)r^2$$

$$(3\sqrt{3}/4)r^2 = 16\sqrt{3}$$

$$r^2=64/3$$

Area of circle will be 64π/3

Hence C
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Director
Joined: 06 Jan 2015
Posts: 586
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: An equilateral triangle that has an area of 16√ 3 is inscribed in a ci  [#permalink]

### Show Tags

05 Oct 2018, 19:04
Bunuel wrote:
An equilateral triangle that has an area of 16√3 is inscribed in a circle. What is the area of the circle?

(A) 3π

(B) 16π/3

(C) 64π/3

(D) 12√3*π

(E) 20√3*π

Alternate Solution

Area of equilateral triangle = $$(\sqrt{3}/4)a^2$$

$$(\sqrt{3}/4)a^2 = 16\sqrt{3}$$

Side (a) = 8

height $$h = (\sqrt{3}/2)*8$$

Incentre divides height in the ration 2:1

Hence radius = 2/3(height of equilateral triangle)

$$r=2/3(4\sqrt{3})$$

Hence $$r= (8/3)\sqrt{3}$$

Area $$πr^2 = 64π/3$$

Hence C
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Re: An equilateral triangle that has an area of 16√ 3 is inscribed in a ci   [#permalink] 05 Oct 2018, 19:04
Display posts from previous: Sort by

# An equilateral triangle that has an area of 16√ 3 is inscribed in a ci

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.