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

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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.

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.

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.
_________________

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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.

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.

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.

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!