在国内外数学竞赛中,常有一些与圆有关的高难度试题出现.笔者通过类比、研究,发现这些试题的证明若以如下定理为模式,建立有关的关系式,则证明简捷明快. In mathematics competitions at home and abroad, there are often high difficulty test questions related to circles. Through comparison and research, the author finds that the testimony of these test questions is based on the following theorem and establishes related relations.