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形如b/a=c~2/b~2(a、b、c、d表示线段)的比例的证明,同学们常感到棘手,本文举例说明说它的一种证明方法—凑比法。其思路是将b/a凑成b/x·x/a,若待定线段x使得b/x=c/d且x/a=c/d,则b/a=b/x·x/a=c~2/d~2。例1 如图1,自⊙O外一点P作⊙O的切线PA,过P作割线PCB,求证:PB/PC=(AB)~2/(AC)~2 分析:设PB/PC=PB/x·x/PC(x为待定线段),先证明PB/x=AB/Ac,由此确定出x,再证明
For example, the proof of the ratio of b/a=c~2/b~2 (a, b, c, and d indicates the line segment), the students often find it difficult to do so. This article gives an example to illustrate its method of proof-comparison. The idea is to make b/a into b/x·x/a. If the line x is to be x so that b/x=c/d and x/a=c/d, then b/a=b/x·x/a =c~2/d~2. Example 1 As shown in Fig. 1, a point P is used as the tangent line PA of ⊙O, and P is used as the secant PCB. Proof: PB/PC=(AB)~2/(AC)~2 Analysis: Set PB/PC= PB/x·x/PC (x is the line to be determined), first prove that PB/x=AB/Ac, from which x is determined, and then prove