Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 May 2017, 21:10

### 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

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 June
Open Detailed Calendar

# What is the measure of the radius of the circle that circums

Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Jan 2010
Posts: 28
Schools: Kellogg, Booth, Harvard, Wharton, Stanford
WE 1: Product Strategy
WE 2: Operations
WE 3: Entrepreneurship
Followers: 0

Kudos [?]: 11 [0], given: 1

What is the measure of the radius of the circle that circums [#permalink]

### Show Tags

23 Jan 2010, 11:50
4
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

79% (01:51) correct 21% (01:18) wrong based on 163 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Nov 2013, 03:38, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 13 Oct 2009
Posts: 116
Location: USA
Schools: IU KSB
Followers: 4

Kudos [?]: 88 [0], given: 66

Re: Geometry - Triangle circumscribed in a circle [#permalink]

### Show Tags

23 Jan 2010, 12:18
1
This post was
BOOKMARKED
shuj00 wrote:
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
6
4
24.5
20.5
12.5
The correct choice is (D) and the correct answer is 20.5.

Triangle with sides 9, 40 and 41 is a right triangle

$$40^2+9^2 = 41^2$$

A right triangle incribed inside a circle - longest side of the triangle will be the diameter of the circle.

so dia of circle is 41 and so the redius is 20.5
Intern
Joined: 21 Jan 2010
Posts: 49
Followers: 0

Kudos [?]: 34 [2] , given: 0

Re: Geometry - Triangle circumscribed in a circle [#permalink]

### Show Tags

23 Jan 2010, 12:24
2
KUDOS
First, you can determine that you have a right triangle:

40^2 + 9^2 = 41^2

Because you have a right triangle, the 'circumcenter' of is on the hypotenuse. What this means is that the center of the circle lies on the hypotenuse of the right triangle. Because the 'circumcenter' is determined by the perpendicular bisectors of the midpoint of each side of the right triangle, we know that the circumcenter is at the midpoint of the hypotenuse.

Because we know that the hypotenuse of the right triangle goes through the center of the circle, the length of the hypotenuse is also the diameter of the circle. So, the radius is half the length of this side of the triangle.

Thus, 41 / 2 = 20.5.

There is a much better explanation on Wikipedia - search for 'Circumscribed circle' (I can't post links yet).
_________________

________________________________________________________________________
Andrew
http://www.RenoRaters.com

Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 612
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Followers: 78

Kudos [?]: 498 [0], given: 298

Re: Geometry - Triangle circumscribed in a circle [#permalink]

### Show Tags

22 Nov 2013, 03:21
swatirpr wrote:
shuj00 wrote:
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
6
4
24.5
20.5
12.5
The correct choice is (D) and the correct answer is 20.5.

Triangle with sides 9, 40 and 41 is a right triangle

$$40^2+9^2 = 41^2$$

A right triangle incribed inside a circle - longest side of the triangle will be the diameter of the circle.

so dia of circle is 41 and so the redius is 20.5

Bunuel Boss any better approach I solved the same way as mentioned above.

I sit essential that longest side will be diameter?
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Math Expert
Joined: 02 Sep 2009
Posts: 39040
Followers: 7750

Kudos [?]: 106484 [2] , given: 11626

Re: Geometry - Triangle circumscribed in a circle [#permalink]

### Show Tags

22 Nov 2013, 03:44
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
honchos wrote:
swatirpr wrote:
shuj00 wrote:
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
6
4
24.5
20.5
12.5
The correct choice is (D) and the correct answer is 20.5.

Triangle with sides 9, 40 and 41 is a right triangle

$$40^2+9^2 = 41^2$$

A right triangle incribed inside a circle - longest side of the triangle will be the diameter of the circle.

so dia of circle is 41 and so the redius is 20.5

Bunuel Boss any better approach I solved the same way as mentioned above.

I sit essential that longest side will be diameter?

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.

Hope it's clear.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2181 [0], given: 193

Re: What is the measure of the radius of the circle that circums [#permalink]

### Show Tags

10 Mar 2014, 20:07

Attachments

cir.jpg [ 34.64 KiB | Viewed 4013 times ]

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15503
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: What is the measure of the radius of the circle that circums [#permalink]

### Show Tags

11 Jan 2016, 20:52
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] 11 Jan 2016, 20:52
Similar topics Replies Last post
Similar
Topics:
2 If the radius of the circle pictured above is 1, what is the measure 7 12 Mar 2017, 19:22
If the radius of the circle with centre O is 7 and the measure of angl 3 18 May 2016, 10:48
2 What is the radius of the circle? 5 10 Jul 2011, 05:05
11 What is the measure of the radius of the circle inscribed in a triangl 12 20 Feb 2017, 00:13
17 What is the measure of the radius of the circle that circums 15 10 Mar 2014, 12:05
Display posts from previous: Sort by