(本小題滿分10分)選修4—1:幾何證明選講
如圖,四邊形
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是邊長為
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的正方形,以
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為圓心,
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為半徑的圓弧與以
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為直徑的半圓
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交于點
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,延長
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交
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于
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.

(1)求證:
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是

的中點;
(2)求線段
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的長.
(1)證明見解析(2)
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試題分析:(1)證明:連結(jié)
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,則
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,
因為
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是的切線,且
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是圓
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的弦,
所以
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,即
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,
故
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,所以
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; ---5分
(2)連結(jié)
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,則由
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,得
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,
所以
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. ---10分
點評:這部分知識涉及到初中平面幾何的知識,要注意靈活應(yīng)用.
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(本小題滿分10分)選修4-1:幾何證明選講
如圖所示,已知
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與⊙
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相切,

為切點,

為割線,
弦

,
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、
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相交于
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點,
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為

上一點,且

·
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.

(1)求證:

;
(2)求證:

·

=
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·
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.
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如圖,
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為⊙

的直徑,

,弦
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交
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于點
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.若
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,

,則
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_____.

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(本小題滿分10分)
如圖,已知
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是
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的切線,
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為切點,

是

的割線,與
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交于

兩點,圓心

在

的內(nèi)部,點
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是

的中點.

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
四點共圓;
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
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
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
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
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
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
,

,

,

是圓

的切線,則

_______.

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