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

Revision as of 07:46, 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.

@@ 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>
 Prove that if the triangle is isosceles.