2
Part of 1998 Irish Math Olympiad
Problems(2)
nice exercise (maybe posted before)
Source: Ireland 1998
7/4/2009
The distances from a point inside an equilateral triangle to the vertices of the triangle are , and . Find the area of the triangle.
geometrygeometric transformationrotationtrigonometrygeometry proposed
nice inequality
Source: Ireland 1998
7/4/2009
Prove that if are positive real numbers, then:
\frac{9}{a\plus{}b\plus{}c} \le 2 \left( \frac{1}{a\plus{}b}\plus{}\frac{1}{b\plus{}c}\plus{}\frac{1}{c\plus{}a} \right) \le \frac{1}{a}\plus{}\frac{1}{b}\plus{}\frac{1}{c}.
inequalitiesinequalities proposed