MathDB

2

Part of 2004 Austrian-Polish Competition

Problems(1)

Austra-Poland triangle inequality

Source: Austra-Poland 2004, single competition, problem 2

2/15/2005
In a triangle ABCABC let DD be the intersection of the angle bisector of γ\gamma, angle at CC, with the side AB.AB. And let FF be the area of the triangle ABC.ABC. Prove the following inequality: 2⋅ F⋅(1AD−1BD)≤AB.2 \cdot \ F \cdot \left( \frac{1}{AD} -\frac{1}{BD} \right) \leq AB.
inequalitiesgeometrytrigonometryangle bisectorgeometry solved