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【原创】数学篇（W）——又一个三角形中的几何不等式猜想

2014-09-26 06:08:07| 分类：默认分类 | 标签： |举报 |字号大中小订阅

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在三角形ABC中，以ma等，wa等，ra等，s分表其中线，角平分线，旁切圆半径和半周，∑表循环和，则猜想有

(∑ma)^2≥2*s^2*[∑ra/(wa+ra)]≥(∑wa)^2 (*)

成立，又

(*)式可改写成等价形式

2*[(∑wa)/(∑a)]^2≤∑ra/(wa+ra)≤2*[(∑ma)/(∑a)]^2 (**)

注 (*)式实质给出了∑ma与∑wa的一个优美的隔离.

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