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证明平面几何定值问题的关键,在于分析动点或动线段、固定量与推证结论之间的相依关系。对于证较复杂的平几定值问题的有效方法之一,就是把条件中的动点或动线段放在图形中的某一特殊位置上,先探求出其定值,然后加以证明。兹举数例如下,予以说明。例1 已知半径为R的圆O的两条平行切线AC与BD,A、B分别为切点。又圆O的另一条动切线与AC交于C,与BD交于D。求证:两线段AC与BD的乘积为一常量。图1分析:为了预测定值,把动切线选定与AB平行时的特殊位置,显然ABDC为一矩形,AC·BD=
The key to prove the problem of plane geometry setting is to analyze the relationship between dynamic point or moving line segment, fixed quantity and inference result. One of the effective methods for verifying the complex fixed-value setting problem is to place the moving point or moving line segment in the condition in a special position in the graph, find the fixed value first, and then prove it. For illustration, please refer to the examples below. Example 1 It is known that two parallel tangents AC and BD, A and B of a circle O with a radius R are tangent points, respectively. The other tangent line of circle O is also intersected with AC at C and with BD at D. Prove that the product of the two line segments AC and BD is a constant. Figure 1 Analysis: In order to predict the fixed value, the special position when the tangent line is selected in parallel with AB, apparently ABDC is a rectangle, AC · BD =