文[1]和文[2]对三角形重心进行了探究,阅读之后受到启发,笔者发现三角形内心也有类似的性质,现行之成文与读者共同探讨.性质1如图1,设△ABC的三个顶点A,B,C所对的三边长分别为a,b,c.已知点I是△ABC的内心,过I作直线与AB,AC两边分别交于M,N两点,且AM=m AB,AN=n AC,则bm+cn=a+b图 The paper [1] and [2] explored the triangle center of gravity and was inspired after reading. The author finds that the triangle heart has similar properties. The current essay is discussed with readers. Property 1 is shown in Fig. 1. Let ΔABC have three vertices. The lengths of the three sides A, B, and C are respectively a, b, and c. The known point I is the inner center of △ABC, and the lines I and AB and AC cross each other at two points M and N, and AM= m AB,AN=n AC,bm+cn=a+b