如圖,
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是圓的內(nèi)接四邊形,
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,過
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點的圓的切線與

的延長線交于

點,證明:

(Ⅰ)
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(II)
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試題分析:(Ⅰ)利用弦切角定理證明
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;(II)轉(zhuǎn)化為等積式,利用三角形相似來證明.
試題解析:證明:(Ⅰ)
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與圓相切于點
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,
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.
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
,
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,
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.

(Ⅱ)
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,
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,
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.
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是圓的內(nèi)接四邊形,
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
, 又
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,

∽
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,
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
,
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.
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科目:高中數(shù)學
來源:不詳
題型:解答題
如圖,AB是⊙O的直徑,AC是弦,∠BAC的平分線AD交⊙O于點D,DE⊥AC,交AC的延長線于點E,OE交AD于點F.

(I)求證:DE是⊙O的切線;
(II)若

=

,求

的值.
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科目:高中數(shù)學
來源:不詳
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如圖所示,梯形ABCD的對角線交于點O,則下列四個結論:

①△AOB∽△COD;
②△AOD∽△ACB;
③S
△DOC∶S
△AOD=CD∶AB;
④S
△AOD=S
△BOC.
其中正確的個數(shù)為( ).
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科目:高中數(shù)學
來源:不詳
題型:解答題
如圖,

的內(nèi)心為

,

分別是

的中點,

,內(nèi)切圓

分別與邊

相切于

;證明:

三線共點.

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科目:高中數(shù)學
來源:不詳
題型:解答題
如圖,⊙

的半徑為3,兩條弦
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,

交于點

,且

,

,

.
求證:△

≌△
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.

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科目:高中數(shù)學
來源:不詳
題型:解答題
如圖,

是圓

的直徑,

為圓上一點,

,垂足為

,點

為圓

上任一點,

交于點

,

交

于點

.

求證:(1)

;(2)

.
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科目:高中數(shù)學
來源:不詳
題型:解答題
如圖,已知

為銳角△

的內(nèi)心,且

,點

為內(nèi)切圓

與邊

的切點,過點

作直線

的垂線,垂足為

.

(1)求證:

;
(2)求

的值.
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科目:高中數(shù)學
來源:不詳
題型:填空題
如圖,圓

的割線

交圓

于

、

兩點,割線

經(jīng)過圓心.已知

,

,

.則圓

的半徑

.

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科目:高中數(shù)學
來源:不詳
題型:填空題
如圖,

是半圓

的直徑,

是半圓

上異于

的點,

,垂足為

. 若

,

,則
.
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