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在人教A版必修二第124页有这样一个习题:平面直角坐标系中有A(0,1),B(2,1),C(3,4),D(-1,2)四点,这四点能否在同一个圆上?为什么?判断四点共圆,方法很多,教师用书中给出的解答是先求出经过A,B,C三点的圆的方程,再把点D的坐标代人圆的方程检验,从而证明了四点共圆.如果把问题推广到一般情况,给出四个点,不需要求出过三点的圆的方程,能否通过它们的坐标联系直接来判断四点是否共圆呢?经过一番推导,笔者发现如下:性质平面直角坐标系中有A(x_A,y_A),B(X_B,y_B),C(X_C,y_C),D(x_D,y_D)四点(任意三点不
There is an exercise on the 124th page of the Second Edition of Pedagogic A. There are A(0,1), B(2,1), C(3,4), D(-1,2) four in the Cartesian coordinate system. Can these four points be in the same circle? Why? Judging four points to be co-circular, there are many methods. The answer given in the teacher’s book is to first find the equation of the circle passing A, B, C, and then The coordinates of the coordinates of the point D are tested by the equation of the circle, which proves that the four points are co-circular. If the problem is generalized to the general situation, four points are given, and it is not necessary to find the equation of the three-point circle. Can they pass through them? Coordinates directly to determine whether the four points are co-circular it? After some deduction, the author found as follows: Character plane A Cartesian coordinate system A (x_A, y_A), B (X_B, y_B), C (X_C, y_C), D (x_D, y_D) four points (any three points are not