(本小題12分)如圖,四棱椎
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的底面為菱形,且
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,
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平面
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,
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,
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為
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的中點(diǎn).
(1)求直線
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與平面
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所成角的正切值;
(2)在線段
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上是否存在一點(diǎn)
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,使
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面
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成立?如果存在,求出
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的長;如果不存在,請說明理由.
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(1)如圖,連結(jié)
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交于點(diǎn)
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,
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,又
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底面
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是菱形,
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,連結(jié)
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,則
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為
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與平面
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所成的角,所以
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=
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(2)過點(diǎn)
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作
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于
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,由
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得
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,因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823142426651236.gif" style="vertical-align:middle;" />在底面
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上的射影為
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且
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所以
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,又
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,所以
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所以,所求
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存在,且使
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。
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已知四邊形
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是邊長為
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的正方形,
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分別為
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的中點(diǎn),沿
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將
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向同側(cè)折疊且與平面
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
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;
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與平面

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
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的中點(diǎn).
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所成的角;
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”,類比上述處理方法,可得該三棱錐的外接球半徑為
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