正文 第三十六章 学神放大招，构造法！(第1页/共3页)
蔡见森不肯相信，忙低头去细看这秦克的证明过程。
一看到秦克作的辅助线，蔡见森顿时松了口气，同时心头狂喜，这家伙做错了！这和他手里的标准答案不一样！
蔡见森简直要放声大笑，难怪这小子的证明过程不到二十行，原来是做错了！
第一步画的辅助线就错了！
居然取AB的中点E，CD的中点F，来作辅助线，分别连接FN、FE、FQ、FO、FM，再连接EN、EF、EO、EM、EQ，还连接了DQ、DB、CA、AQ、CQ，简直是……简直是……乱七八糟，一塌糊涂，这就是你嚣张的代价！居然不用草稿纸，直接在卷子上乱画！
咦，慢着……
这辅助线虽然画得比较多比较复杂，但似乎有点道理，不像是乱画的。
蔡见森不由看向这小子写的证明过程：
“证明：由⊙O1、⊙O2为等圆及劣弧AQ、BQ所对圆周角均为∠BPQ，可得出AQ=BQ。
同理可得QC=QD，又因为劣弧PQ所对圆周角∠PAQ=∠PDQ，可得出
△BQA相似于△CQD，推导出∠AQB=∠CQD
……
由此推导出AC=BD，
可得出NEMF为菱形，推导出M、N在EF的中垂线上……”
蔡见森越看脸色越黑，因为他发现这小子用的方法很不一般，是通过改为证明O点在EF的中垂线上，由此证明M、N、O三点共线！
居然比他做出来的证明方法还要简捷易懂！
这小子用的……居然是奥数里的“构造法”！
蔡见森彻底呆住了。
“构造法”是奥数里一个很重要的解题思维。
它是指根据题设条件和结论的特征、性质，从新的角度，用新的观点去观察、分析、理解对象，然后运用已知数学关系式和理论为工具，在思维中构造出满足条件或结论的数学对象，使原问题中隐含的关系和性质在新构造的数学对象中清晰地展现出来，并借助该数学对象方便快捷地解决数学问题的方法。
一般在实际解题过程中，主要的构造法有三种，把题设条件中的关系构造出来，或者将这些关系设想在某个模型上得到实现，或者把题设条件经过适当的逻辑组织而构造出一种新的形式。
构造法经历过德国克隆尼克的“直觉数学阶段”，马尔科夫的“算法数学阶段”，才进入比肖泊的“现代构造数学阶段”，由此得到推广使用，在高中阶段主要在奥数竞赛中大放异彩。
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