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近年来,随着三角形中一个新的几何度量元素——外心线概念的提出~[1],有关三角形外心线的研究已经取得了许多优秀的成果.最初由文[2]提出了有关外心线的正弦定理;继而由文[1]正式提出了三角形外心线的概念,并做了初步研究;随后,文[3,4]进一步对三角形外心线进行了探讨,并建立了若干有趣的几何不等式.本文继续对三角形的外心线进行研究,得到了如下结果:其一,证明了锐角三角形的三条外心线可以组成一个新的三角形;其二,建立了这个新三角形与原三角形的面积之间、外接圆半径之间的两
In recent years, with the introduction of the concept of the outer line, a new geometric metric element in the triangle, [1] many outstanding achievements have been made in the study of the triangular outer line. Then, the concept of triangular outer line was formally put forward by Wen [1], and a preliminary study was made. Subsequently, the article [3,4] further explored the triangular outer line and established Some interesting geometric inequalities.This paper continues to study the outer concentric lines of the triangle and obtains the following results: First, it is proved that the three outer lines of the acute triangle can form a new triangle; secondly, the new triangle The area between the original triangle, circumscribed circle radius of two