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文[1]为了证明不等式三角形若干“心”的一个性质,给出以下引理:引理设不等边△ABC的外心为O,垂心为H,内心为I,界心为K,则OI=∥12KH.本文拟用向量法将其推广到非等边双圆闭折线中.定理设非等边双圆闭折线的外心为O,垂心为H,内心为I,奈格尔点(即界心)为K,则OI=n-11NH.证明设非等
In [1] in order to prove a property of some “hearts” of the inequality triangle, the following lemma is given: Lemma is assumed that the outer side of the ABC is O, the heart is H, the heart is I, and the center is K. OI=∥12KH. This paper intends to use vector method to generalize it to non-equal-edge double-circle closed lines. The theorem is non-equilateral and double-circular. The outer line of the closed line is O, the vertical center is H, the inner center is I, and the inner point is Nigel Point. (that is, the center of the circle) is K, then OI=n-11NH. The proof is not equal.