Difference between revisions of "1966 IMO Problems/Problem 2"

(Created the page "1996 IMO Problems/Problem 2)
 
m
Line 1: Line 1:
Let <math>A</math>, <math>B</math>, and <math>C</math> be the lengths of the sides of a triangle, and \[ a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta respectively, the angles opposite these sides.  
+
Let <math>A</math>, <math>B</math>, and <math>C</math> be the lengths of the sides of a triangle, and <math> \alpha,\beta,\gamma </math> respectively, the angles opposite these sides.  
  
 
<cmath> a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta}) </cmath>
 
<cmath> a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta}) </cmath>
  
 
Prove that if the triangle is isosceles.
 
Prove that if the triangle is isosceles.

Revision as of 06:46, 5 July 2011

Let $A$, $B$, and $C$ be the lengths of the sides of a triangle, and $\alpha,\beta,\gamma$ respectively, the angles opposite these sides.

\[a+b=\tan{\frac{\gamma}{2}}(a\tan{\alpha}+b\tan{\beta})\]

Prove that if the triangle is isosceles.