三角形周长平分弦的特性

Properties of Perimeter Bisection Chords of Triangles

利用凸集理论和函数极值 ,讨论了三角形周长平分弦关于等周问题的结果 :三角形的任一周长平分弦 L将其划分为 2部分 ,记 ML 为面积较大者 ,S( ML)为 ML 的面积 ,则必存在一弦 L0 ,使得 S( ML0 ) =max{ S( ML)∶ L为周长平分弦 } .研究了三角形周长平分弦的性质 ,得出任一三角形均可确定其最长和最短周长平分弦 .

Using convex theory and extreme value of function,get a result about the perimeter bisection chord of a triangle on isoperimetric problem:Any bisection chord L of a triangle dissects the triangle into two parts,denote M L the one with larger area,S(M L) the area of M L,then there exists a chord L 0,which satisfies:S(M L 0)=max{S(M L):L is a perimeter bisection chord}.Discuss the properties of the perimeter bisection chord of a triangle,give any triangle,its longest and shortest bisection chords can be determined.