# Find the triangle

1. Dec 31, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
If in any triangle r=r1-r2-r3, then which type of triangle is it?

3. The attempt at a solution

4R = r1+r2+r3-r

r2+r3 = 2R

I can't figure out what to do next.

2. Dec 31, 2013

### vela

Staff Emeritus
What are ex-radii? I've never heard that term before. Also, what are $r$ and $R$ supposed to denote?

3. Dec 31, 2013

### Pranav-Arora

Less encountered in geometry problems but they do exist. :)

http://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle

Hi utkarshakash! :)

You are almost there. Can you express $r_2$ and $r_3$ in terms of R, the sines and cosines of three angles of the triangle?

4. Jan 1, 2014