本文对一道初中数学竞赛试题的解法进行了探索,从图形的基本特征入手,抓住关键条件,通过构造直角三角形、正方形或辅助圆,给出了多种自然解法,从而培养学生数学思维的广度与深度,使学生运用所学知识分析问题和解决问题时能够举一反三,达到事半功倍的效果. This article explores the solution of a middle school mathematics competition question. Starting from the basic characteristics of graphics, we grasp the key conditions and construct a variety of natural solutions by constructing right triangle, square or auxiliary circle, so as to cultivate students’ breadth of mathematical thinking And depth, so that students use the knowledge learned to analyze and solve problems can give top priority to achieve a multiplier effect.