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:

Re: circumscribe triangle [#permalink]
10 May 2009, 23:03

2

This post received KUDOS

Some of pyhtagron triplets we need to keep it in mind. Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61). ( 9, 40, 41) is also an Pythagron triplet always appears on the GMAT probs.

So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.

The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 41 / 2 = 20.5

Re: circumscribe triangle [#permalink]
12 May 2009, 06:27

1

This post received KUDOS

1

This post was BOOKMARKED

Thanks Asimov for correcting me. Here is a consolidated list of all the common Pythogron triplets. (3,4,5) (5,12,13)(7,24,25)(8,15,17)(9,40,41)(11,60,61)(12,35,37)(16,60,65)(20,21,29)

That all. I just put them together.incase u might need them.

Re: circumscribe triangle [#permalink]
12 May 2009, 07:29

whats the best way to find the diameter of a circle with an inscribed triangle if you are given an arc? so lets say an inscribed triangle with an arc of 24 that is approximately 3/4ths of the circumference. any suggestions?

Re: circumscribe triangle [#permalink]
26 Aug 2009, 13:28

If I understood you correctly,you mean to say one side of the inscribed triangle creates an arc equal to 24 which is approx 3/4 of the circumference.

If the above understanding is correct, the solution is pretty simple . circumference = 24 * 4/3 = 32 2*pi*r=32 d*pi=32 d=32/pi

dakhan wrote:

whats the best way to find the diameter of a circle with an inscribed triangle if you are given an arc? so lets say an inscribed triangle with an arc of 24 that is approximately 3/4ths of the circumference. any suggestions?

Re: circumscribe triangle [#permalink]
26 Aug 2009, 21:54

Expert's post

I think it is not necessary to know that this triangle is a right triangle.

My 10sec approach. Any sides of a circumscribed triangle is equal or less than a diameter of the circle that circumscribes the triangle. In our case we have a long and thin triangle, so the answer will be 41/2 or something a bit larger. Let's look our options... only B fits. _________________

Re: circumscribe triangle [#permalink]
27 Aug 2009, 02:47

walker wrote:

I think it is not necessary to know that this triangle is a right triangle.

My 10sec approach. Any sides of a circumscribed triangle is equal or less than a diameter of the circle that circumscribes the triangle. In our case we have a long and thin triangle, so the answer will be 41/2 or something a bit larger. Let's look our options... only B fits.

Awesome. Well, thats how I thought. But something came in my mind. How can we consider the largest side as the diameter of the circle without knowing that the triangle is a right angled one? What I mean to say is, if we do consider the largest side as a diameter 41, in this case, isn't it possible that the other two points can lay either within or outside the circle but not on the circle. I dont know how correct I am. But the answer would definately help.

You are awesome with Quant, thats for sure. _________________

GMAT offended me. Now, its my turn! Will do anything for Kudos! Please feel free to give one.

Re: circumscribe triangle [#permalink]
27 Aug 2009, 03:50

Expert's post

bhanushalinikhil wrote:

...How can we consider the largest side as the diameter of the circle without knowing that the triangle is a right angled one? What I mean to say is, if we do consider the largest side as a diameter 41, in this case, isn't it possible that the other two points can lay either within or outside the circle but not on the circle. I dont know how correct I am. But the answer would definately help.

When I said "41/2 or a bit larger" I missed to mention one thing. There are my thoughts in detail.

First of all, diameter cannot be smaller than 41/2, otherwise it would be impossible to circumscribe the triangle by the such small circle. So, we have two options: 41 (B radius = 20.5) or 90 (E radius = 45). 90 is more than twice greater than the biggest side of triangle. It would be possible for triangle with one angle >>90 (for example, 40, 48.5, 9). In our case, we have one small angle (between 41 and 40) and two angle near 90. So only B is an option. It is fast method to figure out an answer with 98% accuracy (let's say a fast guessing technique). But if you have time, it is always possible to spend remaining 2 mins on getting 100% accuracy. You may ask me what if E would be 21? Yeah, this approach doesn't work but for this particular problem it helps save at least 1:30 for next hard question. So, If GMAT wants to trick us, why we cannot trick it? _________________

Re: circumscribe triangle [#permalink]
27 Aug 2009, 04:22

walker wrote:

bhanushalinikhil wrote:

...How can we consider the largest side as the diameter of the circle without knowing that the triangle is a right angled one? What I mean to say is, if we do consider the largest side as a diameter 41, in this case, isn't it possible that the other two points can lay either within or outside the circle but not on the circle. I dont know how correct I am. But the answer would definately help.

When I said "41/2 or a bit larger" I missed to mention one thing. There are my thoughts in detail.

First of all, diameter cannot be smaller than 41/2, otherwise it would be impossible to circumscribe the triangle by the such small circle. So, we have two options: 41 (B radius = 20.5) or 90 (E radius = 45). 90 is more than twice greater than the biggest side of triangle. It would be possible for triangle with one angle >>90 (for example, 40, 48.5, 9). In our case, we have one small angle (between 41 and 40) and two angle near 90. So only B is an option. It is fast method to figure out an answer with 98% accuracy (let's say a fast guessing technique). But if you have time, it is always possible to spend remaining 2 mins on getting 100% accuracy. You may ask me what if E would be 21? Yeah, this approach doesn't work but for this particular problem it helps save at least 1:30 for next hard question. So, If GMAT wants to trick us, why we cannot trick it?

Re: circumscribe triangle [#permalink]
10 Mar 2014, 10:09

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: What is the measure of the radius of the circle that circums [#permalink]
10 Mar 2014, 11:05

Expert's post

What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41? (A) 6 (B) 4 (C) 24.5 (D) 20.5 (E) 12.5

First of all we can notice that a triangle whose sides measure 9, 40 and 41 is a right triangle because 9^2 + 40^2 = 41^2.

Next, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle (the reverse is also true: if the diameter of a circle is also the triangle’s side, then that triangle is a right triangle).

Thus the diameter of the circle is the hypotenuse of the triangle --> diameter = hypotenuse = 41 --> radius = 41/2 = 20.5.

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...