Find Type of Triangle Given r1-r2-r3

[utkarshakash]

Homework Statement

If in any triangle r=r1-r2-r3, then which type of triangle is it?
r1,r2,r3 denotes ex-radii.

The Attempt at a Solution

4R = r1+r2+r3-r

r2+r3 = 2R

I can't figure out what to do next.

 

[vela]

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

 

[Saitama]

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

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

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

Homework Statement

If in any triangle r=r1-r2-r3, then which type of triangle is it?
r1,r2,r3 denotes ex-radii.

The Attempt at a Solution

4R = r1+r2+r3-r

r2+r3 = 2R

I can't figure out what to do next.

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?

 

[utkarshakash]

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?

Thanks for your help!