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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae

r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else ....

An equilateral triangle that has an area of 9*root(3) [#permalink]
25 Nov 2010, 01:30

2

This post received KUDOS

Expert's post

rite2deepti wrote:

An equilateral triangle that has an area of \(9\sqrt{3}\) is inscribed in a circle. What is the area of the circle?

A. \(6\pi\) B. \(9\pi\) C. \(12\pi\) D. \(9\pi \sqrt{3}\) E. \(18\pi \sqrt{3}\)

This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae

r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else ....

I'd recommend to know the ways some basic formulas can be derived in geometry rather than memorizing them.

Anyway, \(area_{equilateral}=a^2*\frac{\sqrt{3}}{4}\), where \(a\) is the length of a side --> as given that \(area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=9\sqrt{3}\) then \(a=6\);

Now, given that this triangle is inscribed in circle (not circle is inscribed in triangle). The radius of the circumscribed circle is \(R=a*\frac{\sqrt{3}}{3}=2\sqrt{3}\) (you used the formula for the radius of the inscribed circle \(r=a*\frac{\sqrt{3}}{6}\)) --> \(area_{circle}=\pi{R^2}=12\pi\).

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
27 Nov 2010, 17:50

Use the formula to calculate area of the inscribed circle to the equliateral triangle. Bunuel's guide on Triangles has all the important formulae in it..

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
18 Dec 2012, 03:32

Formula Triangle inscribed in a circle. area of the triangle inscribed in a circle with radius "r" = (abc)/4r a,b,c - are the sides of a triangle inscribed r - is the radius of the circle.

Circle inscribed in a Triangle are of the triangle = (a+b+c)r/2 a,b,c - sides of a triangle r - radius.

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
12 May 2013, 23:03

rite2deepti wrote:

An equilateral triangle that has an area of \(9\sqrt{3}\) is inscribed in a circle. What is the area of the circle?

A. 6pi B. 9pi C. 12pi D. 9pi 3^1/2 E. 18pi 3^1/2

This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae

r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else ....

the above calculation is correct. since 9pi3^1/2= 9pi/3=3pi so the correct answer is D.

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
13 May 2013, 00:27

rite2deepti wrote:

An equilateral triangle that has an area of \(9\sqrt{3}\) is inscribed in a circle. What is the area of the circle?

A. 6pi B. 9pi C. 12pi D. 9pi 3^1/2 E. 18pi 3^1/2

using the area of the triangle we can get the side of the equilateral triangle using area = (\sqrt{3}/4) x a^2 We can get the side as 6.

now we have the sine formula for the triangle. ie a/sinA = 2R. where R the circumradius of the triangle. a is the side and A is the corresponding angle.

We have A = 60 a = 6 we can get R.which will be 2\sqrt{3}. So the area of the circle will be 12 pi _________________

"Kudos" will help me a lot!!!!!!Please donate some!!!

Completed Official Quant Review OG - Quant

In Progress Official Verbal Review OG 13th ed MGMAT IR AWA Structure

Yet to do 100 700+ SC questions MR Verbal MR Quant

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
13 May 2013, 00:28

khosru wrote:

rite2deepti wrote:

An equilateral triangle that has an area of \(9\sqrt{3}\) is inscribed in a circle. What is the area of the circle?

A. 6pi B. 9pi C. 12pi D. 9pi 3^1/2 E. 18pi 3^1/2

This is how I solved it area of equilateral triangle =Square root 3/4*a^2=9 square root 3 we get a =6 know to calculate radius of an equlateral triangle in an inscribed circle we can use formulae

r=a*square root 3/6 with this I get r=square root 3 and then area =3 pi but its not in the answer choices OA is something else ....

the above calculation is correct. since 9pi3^1/2= 9pi/3=3pi so the correct answer is D.

The correct answer cannot be D...the answer must be C... from the formula of area of triangle you can calculate the side of triangle ie 6. Now the radius of circumcircle (for equilateral triangle) is side/root(3) So substitute to get the final answer ie C

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
28 Jul 2013, 22:37

rite2deepti wrote:

An equilateral triangle that has an area of \(9\sqrt{3}\) is inscribed in a circle.

I am trying to relearn about the term "inscribed". Please help: Does "inscribed" mean all the edges of the triangle are just touching the circle or can it mean that the trianlge lies completely inside the circle (meaning the edges need not touch the circle and can range from very small size to size that exactly fits in the circle).

In some questions I have seen that it is necessary to assume that inscribed means the triangle completely lies inside (and not necessarily have the edges touch the circle) while for this question is means a perfectly inscribed triangle. Same doubt applies for circumscribed as well.

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
28 Jul 2013, 22:44

Expert's post

Jaisri wrote:

rite2deepti wrote:

An equilateral triangle that has an area of \(9\sqrt{3}\) is inscribed in a circle.

I am trying to relearn about the term "inscribed". Please help: Does "inscribed" mean all the edges of the triangle are just touching the circle or can it mean that the trianlge lies completely inside the circle (meaning the edges need not touch the circle and can range from very small size to size that exactly fits in the circle).

In some questions I have seen that it is necessary to assume that inscribed means the triangle completely lies inside (and not necessarily have the edges touch the circle) while for this question is means a perfectly inscribed triangle. Same doubt applies for circumscribed as well.

A triangle inscribed in a circle does NOT mean that it is simply "inside" the circle, it means that the triangle's vertices are on the circumference of the circle. _________________

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
29 Jul 2013, 07:21

Bunuel wrote:

A triangle inscribed in a circle does NOT mean that it is simply "inside" the circle, it means that the triangle's vertices are on the circumference of the circle.

Thanks for the clarification Bunuel! Seeing the explanation " The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: P>0." in http://gmatclub.com/forum/which-of-the-following-can-be-a-perimeter-of-a-triangle-68310.html, I mistakenly assumed the triangle has to just lie inside the circle. I now understand that the triangle's edges should touch the circle and have perimeter >0. Thanks again!

Re: An equilateral triangle that has an area of 9*root(3) [#permalink]
12 Jul 2014, 11:26

Expert's post

manish2014 wrote:

Hi Bunnel,

My logic-- side of equi triangle --6

now, the formula for area of a inscribed trianle is (p.r)/2=9sqrrt(3)

p=6+6+6=18

therefore r=sqrt(3)

there area(circle)=pi.3

is this incorrect?

Since your answer does not match any of the options, then obviously you are doing something wrong there. Also, I don't know what kind of formula you are using in your solution... _________________

Back to hometown after a short trip to New Delhi for my visa appointment. Whoever tells you that the toughest part gets over once you get an admit is...