定理如图1,△DEF是△ABC的三条外角平分线构成的三角形,△ABC与△DEF的三条中线分别为ma、mb、mc及md、me、mf,则m2d+m2e+mf2≥4(m2a+m2b+m2c)(1)(当且仅当△ABC为正三角形时取等号)约定BC=a,CA=b,AB=c,s=12(a+b+c),EF=d,DF=e,DE=f,△ABC的外接圆与内切圆半径分别为R、r.图1证 Theorem is shown in Figure 1. △DEF is the triangle formed by the three external bisectors of △ABC. The three midlines of △ABC and △DEF are respectively ma, mb, mc, md, me, mf, then m2d+m2e+mf2≥4 ( M2a+m2b+m2c) (1) (If and only if △ABC is an equilateral triangle, take the equal sign) Conventions BC=a,CA=b,AB=c,s=12(a+b+c),EF= d, DF = e, DE = f, △ ABC circumcircle and inscribed circle radius respectively R, r. Figure 1 card