本文通过建立平面直角坐标系,应用解析法对著名的朗古莱定理及其推广进行巧思妙证.朗古莱定理在同一圆周上有A1、A2、A3、A4四点,从其中任意三点作三角形,在圆周上取一点P,作P点的关于这四个三角形的西摩松线,再从P点向这四条西摩松线引垂线,求证:四垂足共线.此直线叫做P点的关 This paper establishes the plane rectangular coordinate system and applies the analytical method to inflect the famous Longgurule theorem and its generalization. The Langulai theorem has four points A1, A2, A3, and A4 on the same circle, from which any three Make a triangle, take a point P on the circumference, make a P-point on the Seymours line of the four triangles, and then pull the vertical line from P to the four Seymoursong lines to verify that four legs are collinear. The straight line is called P point off