题目内容
(本题满分10分)
如图,已知C、F是以AB为直径的半圆
上的两点,且CF=CB,过C作CD^AF交AF的延长线与点D.
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(Ⅰ)证明:CD为圆O的切线;
(Ⅱ)若AD=3,AB=4,求AC的长.
如图,已知C、F是以AB为直径的半圆
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(Ⅰ)证明:CD为圆O的切线;
(Ⅱ)若AD=3,AB=4,求AC的长.
(1)根据圆的切线的定义,只要证明圆心与点C的连线垂直于CD即可。
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(2)
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试题分析:(Ⅰ)证明:∵
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∵
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则
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∵
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(Ⅱ)解:连接
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又
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点评:对于线段的长度的求解,一般运用相似的思想来得到。或者借助于切线长定理等等的知识得到关系式来得到。
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