一个角平分线猜想不等式的证明

A Proof of the Conjectured Inequality on Angular Bisector

应用三角形一个重要的基本不等式,证明了有关三角形内角平分线之和的一个猜想不等式:设wa,wb,wc与s分别是三角形三条内角平分线和半周长,R,r分别为三角形的外接圆半径,则(wa+wb+wc)2s2+102Rr/5+66r2/5.指出了一个相关的值得进一步探讨的问题.

An important basic inequality for triangles is employed to prove a conjectured inequality for the sum of triangle＇ s inner angular bisector： Let wa, wb, wc, s, r, R be the three inner angular bisectors semi-cimmference inradius and circumradius respectively, then（ w ＋ ＋ wb ＋ wc）^2≤s^2 ＋ 102Rr/5 ＋ 66r^2/5. A televant question worthy of further delvement is put forward.