例1(第23届“希望杯”全国数学邀请赛培训题高一41题)△ABC中,已知AB=4,BC=5,AC=6,若点O是△ABC的外心,则→AO.→AC的值是.分析标准解答给出的解法是应用余弦定理、正弦定理和向量数量积的定义,繁琐冗长.事实上,若注意到题设条件AC=6及向量回路A→M→O,便有如下简解.简解取AC的中点M,则必有MO⊥AC, Example 1 In the ABC, AB = 4, BC = 5, AC = 6 are known. If the point O is the outer center of △ ABC, Then the value of  → AO. → AC is 0. The solution given by the analytical standard solution is the application of cosine theorem, the definition of sine theorem and vector quantity product, tedious and verbose.In fact, if we note that the design conditions of AC = 6 and vector Circuit A → M → O, there will be the following brief. Briefly take AC midpoint M, there must be MO ⊥ AC,