Question

已知：如图，⊙O和⊙ 内切于A，直线O 交⊙O 于另一点B、交⊙ 于另一点F，过B点作⊙ 的切线，切点为D

已知：如图，⊙O和⊙ 内切于A，直线O 交⊙O 于另一点B、交⊙ 于另一点F，过B点作⊙ 的切线，切点为D，交⊙O于C点，DE⊥AB，垂足为E.求证：（1）CD=DE；（2）若将两圆内切改为外切，其它条件不变，（1）中的结论是否成立？请证明你的结论.
2002武汉中考
41题

Answer 1

你的说明有点不清楚，不过图看得满清晰的。

我这样证明的，作辅助线，连接O1D，AD，AC。

因为 O1D垂直BC，AC垂直BC，

所以 O1D平行AC

所以 角O1DA=角DAC

又因为 三角形O1DA的两边O1D=O1A

所以 角O1AD(即角EAD)＝角DAC

因此 三角形EDA全等于三角形CDA

因此 CD=DE

Answer 2

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Answer 3

如图解释，不是很难的

Answer 4

连接AD,AC ,DF
AC垂直BC，DE垂直AF, <DFA=<ADC <ADF=90 所以<DAE=<DAC 且共斜边，故DE=DC
相等
AC垂直BC，DE垂直AF, <DFA=<ADC <ADF=90 所以<DAE=<DAC 且共斜边，故DE=DC