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Triangle ABC is inscribed inside a circle of Radius R .

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prasun84
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Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   23 Nov 2008, 01:39
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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.



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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   23 Nov 2008, 10:02
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.
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   23 Nov 2008, 11:20
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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
https://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.
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   23 Nov 2008, 19:20
how is 6-7-8 a right-angle triangle???


on exam day i would have picked C..
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   23 Nov 2008, 21:59
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.
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   24 Nov 2008, 05:39
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.
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   24 Nov 2008, 10:28
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Radius of an inscribed circle
https://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.

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

https://www.youtube.com/watch?v=NIuMcL4Kz44&fmt=18
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   24 Nov 2008, 12:34
Are you real David interesting in GMAT or his is just your idol? :-D
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   24 Nov 2008, 18:33
atletikos wrote:
Are you real David interesting in GMAT or his is just your idol? :-D

lmao
I'm a girl.
David Archuleta is my idol.
Thanks for asking. :)
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   24 Nov 2008, 23:25
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 :shock: ion (C) at all..
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   26 Nov 2008, 15:56
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!
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   27 Nov 2008, 01:23
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
r->inradius
R->circumradius
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   27 Nov 2008, 07:58
Uhm, I think that all the formula are not neccessary here. :) I chose B right after finishing reading the question.
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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink] New post   28 Nov 2008, 05:05
I got stuck on this one.....what is the source of this question?



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Re: Triangle ABC is inscribed inside a circle of Radius R . [#permalink]
28 Nov 2008, 05:05
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