Triangle ABC is inscribed inside a circle of Radius R .

Question

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.

(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.

DavidArchuleta · Answer

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.

masuhari · Answer

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.

FN · Answer

how is 6-7-8 a right-angle triangle???

on exam day i would have picked C..

GMAT TIGER · Answer

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.

DavidArchuleta · Answer

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.

DavidArchuleta · Answer

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

atletikos · Answer

Are you real David interesting in GMAT or his is just your idol? :-D

DavidArchuleta · Answer

lmao I'm a girl. David Archuleta is my idol. Thanks for asking.

prasun84 · Answer

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..

icandy · Answer

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!

prasun84 · Answer

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

DavidArchuleta · Answer

Uhm, I think that all the formula are not neccessary here.

I chose B right after finishing reading the question.

scthakur · Answer

I got stuck on this one.....what is the source of this question?

Triangle ABC is inscribed inside a circle of Radius R .

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards