我们知道在空间任何不共面的四点必存在唯一的外接球 .那么对于空间五点共球问题又如何判定呢 ?笔者通过研究得出如下具体结论 ,与各位同行商榷 .1　五点共球的充要条件先看如下引理 :引理　如图 1 :Ａ ,Ｂ ,Ｃ是空间不共线的三点 ,以 △ＡＢＣ的外接圆为大圆的球为球Ｏ ,点Ｄ We know that there must be a single circumscribed ball at any four points in space that are not coplanar. Then how do we determine the five-point common ball problem? The author came to the following concrete conclusions through research and discussed it with fellow participants. 1 Five-point ball The necessary and sufficient conditions for the first look at the following lemma: Lemma Figure 1: A, B, and C are the three points where the space is not collinear, and the circumcircle of the ABC is the ball of the big circle.