辛姆生(Simson)定理三角形外接圆上任一点向三边(或其延长线)作垂线,三个垂足共线. 证明1.当△ABC为锐角三角形或钝角三角形时 建立如图1所示的平面直角坐标系,设B,C点的坐标为B(0,0),C(a,0),边AB所在直线方程为y=k1x,边AC所在直线方程为y=k2(x-a),边BC所在直线方程为y=0.从而,顶点A的坐标为方程组 Simson’s Theorem The triangle circumscribes any point on the circle to the three sides (or its extension) as a vertical line, and the three legs are collinear. Proof 1. When △ABC is an acute triangle or an obtuse triangle, it is established as shown in Figure 1. In the rectangular coordinate system shown, set the coordinates of points B and C to B(0,0) and C(a,0), the equation of the edge AB is y=k1x, and the equation of the edge AC is y=k2(xa). ), the equation of the line where BC is located is y = 0. Thus, the coordinates of vertex A are equations