Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 07 Jul 2015, 18:23

### 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

# Triangle ABC is inscribed inside a circle of Radius R .

Author Message
TAGS:
Manager
Joined: 08 Aug 2008
Posts: 234
Followers: 1

Kudos [?]: 22 [0], given: 0

Triangle ABC is inscribed inside a circle of Radius R . [#permalink]  23 Nov 2008, 00:39
00:00

Difficulty:

(N/A)

Question Stats:

100% (02:19) correct 0% (00:00) wrong based on 0 sessions
Triangle ABC is inscribed inside a circle of Radius R. Another circle of Radius r is inscribed inside Triangle ABC. What is the ratio of Radius of the outer Circle to the radius of the Inner circle?

(1)Triangle ABC is a right-angled triangle.
(2)The sides of triangle ABC are 6, 7 and 8.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
Followers: 2

Kudos [?]: 81 [0], given: 40

Re: DS:Circle-triangle [#permalink]  23 Nov 2008, 09:02
prasun84 wrote:
Triangle ABC is inscribed inside a circle of Radius R. Another circle of Radius r is inscribed inside Triangle ABC. What is the ratio of Radius of the outer Circle to the radius of the Inner circle?

(1)Triangle ABC is a right-angled triangle.
(2)The sides of triangle ABC are 6, 7 and 8.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

B for sure
1 just gives us R= 1/2 the longest side of the right-angled triangle while gives nothing about r.
2 gives us 3 sides of a triangle so this triangle exists and are fixed. It has a fixed r and a fixed R. So we don't have to calculate the ration but the ratio is determined.
Intern
Joined: 14 Sep 2003
Posts: 45
Location: california
Followers: 1

Kudos [?]: 15 [1] , given: 0

Re: DS:Circle-triangle [#permalink]  23 Nov 2008, 10:20
1
KUDOS
would have had to guess on this one...I'd have chosen A, but doing a quick search on the web for properties of inscribed circles / triangles, found this link very useful
http://www.ajdesigner.com/phptriangle/r ... dius_r.php

using that info, unless we know the lengths of the sides of the right triangle, we can't calculate the radius $$ab/a+b+c$$

I know we are not looking for r, but the ratio of r to R. So statement #1 alone not sufficient. A and D are incorrect choices.

Given the sides of the scalene triangle, as 6, 7 and 8, we can calculate the radius of the inscribed circle. But since we don't know which this triagle's relationship to R, we can't calculate r to R. So B is out

Together, the statements say we have a right triangle, but the lengths provided in #2 don't fulfil that. Hence C is incorrect as well.

My pick E. curious to know OA. Even if I got it wrong, glad to have run into this problem coz I now know the formula for a circle inscribed within a Right triangle.
_________________

excellence is the gradual result of always striving to do better

Current Student
Joined: 28 Dec 2004
Posts: 3387
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 14

Kudos [?]: 187 [0], given: 2

Re: DS:Circle-triangle [#permalink]  23 Nov 2008, 18:20
how is 6-7-8 a right-angle triangle???

on exam day i would have picked C..
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 579 [0], given: 19

Re: DS:Circle-triangle [#permalink]  23 Nov 2008, 20:59
prasun84 wrote:
Triangle ABC is inscribed inside a circle of Radius R. Another circle of Radius r is inscribed inside Triangle ABC. What is the ratio of Radius of the outer Circle to the radius of the Inner circle?

(1)Triangle ABC is a right-angled triangle.
(2)The sides of triangle ABC are 6, 7 and 8.

Not a very good question as statements 1 and 2 contradicts each other. A traingle with sides 6, 7, and 8 cannot be a right angle triangle.

For me it is E.
_________________
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
Followers: 2

Kudos [?]: 81 [0], given: 40

Re: DS:Circle-triangle [#permalink]  24 Nov 2008, 04:39
masuhari wrote:
Given the sides of the scalene triangle, as 6, 7 and 8, we can calculate the radius of the inscribed circle. But since we don't know which this triagle's relationship to R, we can't calculate r to R. So B is out

I don't think so!
We can calculate R and r of this triangle.
There are some fomula to calculate them I can write them here.
But what I want to say is that this triangle is unique, (2) shows its 3 sides. Every triangle has an inscribed cirle and an outscribed circle. For every given triangle, the circles exist and they are unique like the triangle.
I must go watching movie now.
Write the formula later.
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
Followers: 2

Kudos [?]: 81 [1] , given: 40

Re: DS:Circle-triangle [#permalink]  24 Nov 2008, 09:28
1
KUDOS
http://www.analyzemath.com/Geometry_cal ... ircle.html

The radius of the circumcircle. The radius is given by the formula

where a,b,c are the lengths of the sides of the triangle.

http://www.mathopenref.com/trianglecircumcircle.html

Manager
Joined: 18 Nov 2008
Posts: 117
Followers: 1

Kudos [?]: 10 [0], given: 0

Re: DS:Circle-triangle [#permalink]  24 Nov 2008, 11:34
Are you real David interesting in GMAT or his is just your idol?
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
Followers: 2

Kudos [?]: 81 [0], given: 40

Re: DS:Circle-triangle [#permalink]  24 Nov 2008, 17:33
atletikos wrote:
Are you real David interesting in GMAT or his is just your idol?

lmao
I'm a girl.
David Archuleta is my idol.
Manager
Joined: 08 Aug 2008
Posts: 234
Followers: 1

Kudos [?]: 22 [0], given: 0

Re: DS:Circle-triangle [#permalink]  24 Nov 2008, 22:25
Guys, the OA is B.
had a hard time trying to figure out a conceptual non-formulaic approach but to no availl...

also agree with gmattigers argument that the question seems wrongly constructed...doesnt allow for opt ion (C) at all..
VP
Joined: 05 Jul 2008
Posts: 1431
Followers: 35

Kudos [?]: 260 [0], given: 1

Re: DS:Circle-triangle [#permalink]  26 Nov 2008, 14:56
I ruled out C

But this Q takes it to another level of difficulty. So what this Q is saying is if we know the sides of a triangle, we can find the radii of both the circumcircle (the circle around it) and the inscribed circle. No kidding!
Manager
Joined: 08 Aug 2008
Posts: 234
Followers: 1

Kudos [?]: 22 [0], given: 0

Re: DS:Circle-triangle [#permalink]  27 Nov 2008, 00:23
Guys, heres another formula which might seem useful and convenient:

area of trianble ABC=$$r*s$$=$$abc/4R$$
where a,b,c are sides of a triangle
Manager
Joined: 05 Jul 2008
Posts: 139
GMAT 1: Q V
GMAT 2: 740 Q51 V38
Followers: 2

Kudos [?]: 81 [0], given: 40

Re: DS:Circle-triangle [#permalink]  27 Nov 2008, 06:58
Uhm, I think that all the formula are not neccessary here. I chose B right after finishing reading the question.
SVP
Joined: 17 Jun 2008
Posts: 1570
Followers: 12

Kudos [?]: 203 [0], given: 0

Re: DS:Circle-triangle [#permalink]  28 Nov 2008, 04:05
I got stuck on this one.....what is the source of this question?
Re: DS:Circle-triangle   [#permalink] 28 Nov 2008, 04:05
Similar topics Replies Last post
Similar
Topics:
An equilateral triangle ABC is inscribed in the circle. If 2 23 Apr 2011, 14:32
4 Square R is inscribed in circle C and C is inscribed in 2 14 Feb 2011, 14:50
5 A circle is inside an equalateral triangle ABC. One side of 13 06 Nov 2010, 23:18
19 Circle O is inscribed in equilateral triangle ABC, which is 14 26 Jun 2010, 06:52
Triangle ABC is inscribed in circle D. If the area of D 8 27 Nov 2006, 10:51
Display posts from previous: Sort by