巧妙的解题思路,从具体问题来说,它来自问题的特殊性被得到彻底的揭示.因为只有揭示了问题的特殊性,才能得到未知向己知、生疏向熟悉、条件向结论的转化途径,而转化就是解题.数学问题的特殊性突出表现在“数值特征、结构关系、图像信息”三个方面,挖出它们是快速找到解题途径、巧妙解题的关键!下面举例说明. 一、挖“结构关系” 例1 以线段AB为直径作一个半圆,圆心为O,C为半圆周上的点,有OC2=AC·BC.则∠CAB=(). 简析画图有两种可能,如图1、图2. OC2=AC·BC中,“AC·BC”视为 Rt△ABC Clever problem-solving ideas, from the specific issues, it comes from the specificity of the problem has been completely revealed. Because only reveal the specificity of the problem, we can get the unknown to know, strange to familiar, conditional to the conclusion of the conversion path The transformation is the problem solving. The particularity of the mathematics problem is highlighted in three aspects: “numerical features, structural relationships, and image information”. Excavating them is the key to quickly finding the solution to the problem and ingeniously solving the problems. The following examples illustrate. , Digging the “Structure Relationship” Example 1 Make a semicircle with the diameter of line AB as a circle, the center of the circle is O, and C is the point on the half circle. There is OC2=AC·BC. Then ∠CAB=(). There are two possibilities for the analysis of the drawing. , Figure 2. In OC2 = AC · BC, “AC · BC” is treated as Rt △ ABC