本文研究三角形顶点与对边任一点连线的一个性质 ,因这种线是三角形中线、角平分线、高的推广 ,故其具有一定的价值 .定理 1　如图 1 ,D为△ ABC的 AC边上任一点 (两端点除外 ) ,AB=a,BC=b,CD =c,DA =d,CA =m,DB =n,∠ DAB +∠ DCB =α,∠ DBC =β,∠ DBA =γ,则有( mn) 2 =( a In this paper, we study the nature of the connection between the vertices of a triangle and any point on the opposite side. Because this line is a generalization of the triangle midline, angle bisector, and height, it has a certain value. Theorem 1 As shown in Figure 1, D is AC of △ ABC. Any point on the edge (excluding the two ends), AB=a,BC=b,CD=c,DA=d,CA=m,DB=n,∠ DAB +∠ DCB =α,∠ DBC =β,∠ DBA =γ , there are (mn) 2 = (a