Difference between revisions of "1989 OIM Problems/Problem 2"
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== Problem == | == Problem == | ||
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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> | ||
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| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 13:16, 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
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