如图，AB是⊙O的直径，AC是弦，半径OD⊥AC于点E，过点D的切线与BA延长线交于点F．（1）求证：∠CDB=∠BFD；（2）若AB=10，AC=8，求DF的长．_刷题宝

题干

如图，AB是⊙O的直径，AC是弦，半径OD⊥AC于点E，过点D的切线与BA延长线交于点F．

（1）求证：∠CDB=∠BFD；

（2）若AB=10，AC=8，求DF的长．

上一题下一题 0.0难度选择题更新时间:2019-11-25 04:04:09

答案(点此获取答案解析）

解：（1）∵DF与⊙O相切，

∴DF⊥OD，

∵OD⊥AC，

∴DF∥AC，

∴∠CAB=∠BFD，

∴∠CAB=∠BFD，

∴∠CDB=∠BFD；

（2）∵半径OD垂直于弦AC于点E，AC=8，

∴AE= $\frac{1}{2}$

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