Difference between revisions of "1989 OIM Problems/Problem 2"
(Created page with "== Problem == ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com Let <math>a</math>, <math>b</math>, and <math>c</math> be the longitudes of the sides of a triangle...") |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | |||
Let <math>a</math>, <math>b</math>, and <math>c</math> be the longitudes of the sides of a triangle. Prove: | Let <math>a</math>, <math>b</math>, and <math>c</math> be the longitudes of the sides of a triangle. Prove: | ||
<cmath>\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}</cmath> | <cmath>\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}</cmath> | ||
| + | |||
| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 12:16, 13 December 2023
Problem
Let 
, 
, and 
be the longitudes of the sides of a triangle. Prove:
![\[\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}<\frac{1}{16}\]](http://latex.artofproblemsolving.com/8/1/5/815e94b144f496e813104e2bf97099d86c48b775.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
