The isoperimetric point and the point(s) of equal detour in a triangle

被引：2

作者：

Hajja, Mowaffaq ^{[1
]}

Yff, Peter ^{[1
]}

机构：

[1] Yarmouk Univ, Math Dept, Irbid, Jordan

来源：

JOURNAL OF GEOMETRY | 2007年 / 87卷 / 1-2期

关键词：

isoperimetric point; point of equal detour; Soddy circles;

D O I：

10.1007/s00022-007-1906-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A point P in the plane of triangle ABC is said to be an isoperimetric point if PA + PB + AB = PB+ PC+ BC = PC+ PA+ CA, and is said to be a point of equal detour if PA+ PB-AB = PB+ PC-BC = PC + PA - CA. Incorrect conditions for the existence and uniqueness of such points were given by G. R. Veldkamp in Amer. Math. Monthly 92 (1985) 546-558. In this paper, we use a much simpler approach that yields correct versions of these conditions and that exhibits the relations of these points to the centers of the Soddy circles.

引用

页码：76 / 82

页数：7

共 6 条

[1] PROBLEM OF APOLLONIUS [J].