一个三角形中线不等式猜想的证明

Testifying a Conjecture of an Median Inequality of Triangle

采用三角形不等式中R-r-s方法,证明了作者多年前提出的一个有关三角形的猜想不等式,即有关中线ma,mb,mc与外接圆半径R以及内切圆半径r的不等式:1/ma+1/mb+1/mc≤2(1/R+1/r)/3.

The R- r- s method of triangle inequality is employed to prove the conjecture of a triangle inequality proposed by the author many years ago, which is the reciprocal inequality for median ma, mb, me, the eircumradius R and the radius of the inscribed circle r ： l/ ma ＋ 1/mb ＋ 1/ mc ≤ 2（1/ R ＋ 1/ r ） /3.