锐角三角形的一个不等式链

An Inequality Chain for Acute Triangle

应用重要的R-r-s方法,证明了有关锐角三角形的中线、高线与旁切圆半径的不等式链:设锐角ΔABC的三条中线,三条高线与旁切圆半径分别为ma,mb,mc;ha,hb,hc和ra,rb,rc,则成立不等式:maha+mbhb+mchc≥wbwc+wcwa+wawb≥hara+hbrb+hcrc.提出并应用计算机验证了三个有关的猜想.

The important method of R - r- s is used to prove the inequality chain for the medians altitudes and radii of exinscribed circles of a triangle： Let ma, mb, mc denote the medians of the triangle ABC ; the altitudes ha, hb, hc ; the radii of exinscribed excircles ra, rb, rc ; then holds maha＋mbhb＋mchc≥wbwc＋wcwa＋wawb≥hara＋hbrb＋hcrc. Finally, three relevant conjectures are proposed and verified with the computer.