点到圆上的点的最长(短)距离问题探究

The research of the maximum or minimum distance between the points on the circle and other points

点到圆上的点的距离最值问题是高中数学动态类问题的一个难点,也是近年来高考命题的一个热点。圆上的点是动点,另一点可能是定点,也可能是曲线上的动点。如果是定点,那么它到圆上的点的距离最值如何取得;如果是曲线上的动点,那么它与圆上的点的距离又与哪些变量有关。笔者结合近年高考题、模拟题来对以上问题进行探究。

For a long time,the maximum or minimum distance between the points on the circle and other spots is not only one of difficult problems at senior high school,but also hot issues in recent college entrance examinations.The points on the circle are moving,while other points are fixed or moving on the curve.If it's a fixed point,how can we know the maximum or minimum distance between it and the point on the circle.If it is a moving point on the curve,what are the variables related to the distance?The writer is doing research on this project by combining college entrance examination papers and some simulation exercises in the last few years.