一个几何不等式的加强

An Improvement of the Geometric Inequality

根据一个已知的几何不等式,应用差分代换方法并借助于Maple软件进行计算,证明了下述几何不等式:对△ABC与任意一点P有∑PAw2b+w2c≥2(其中wa,wb,wc为△ABC的内角平分线),给出了它的几个推论,提出并应用计算机验证了两个猜想.

Applying the the well- known geometric inequality and the method of diference snbstitution, and using Maple software to carry on the computation, the .following geometric inequality is to established;For every triangle ABC and an arbitrary point P. we have ∑ PA/wb^2＋wc^2≥√2 （where wa, Wb, wc are the corresponding angle - bisectors of a ABC）, and several corollaries are given. Two two conjectures are proposed and verifed by the computer.