The discussion revolves around identifying the type of triangle based on the relationship involving the ex-radii (r1, r2, r3) and the circumradius (R). The original poster presents a mathematical expression relating these elements but is uncertain about the next steps in their reasoning.
Some participants have provided clarifications regarding the terms used in the problem, and one participant suggests expressing certain variables in terms of the circumradius and trigonometric functions. The discussion appears to be progressing with helpful guidance being offered.
There is a noted lack of familiarity with the concept of ex-radii among some participants, which may affect their understanding of the problem. The original poster's expressions involve specific relationships that may require further exploration or clarification.
vela said:What are ex-radii? I've never heard that term before. Also, what are ##r## and ##R## supposed to denote?
utkarshakash said: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.
Pranav-Arora said: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?