1 . 15(几何证明选讲选做题)如图,
是圆
的直径,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd41df221293d5cdbab35be6ae5987e.png)
______
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/6dd94026e36a43a1b1eb042f9fe3dfca.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/03fd77017d714b17b8152e4a47c614e2.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/797c984e40ed4074a9de99b557e9f1cc.png?resizew=68)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/8021a76cfd17480ba5e4d7239a7419a5.png?resizew=103)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd41df221293d5cdbab35be6ae5987e.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572247535755264/1572247541481472/STEM/0a2644f1caf54e728fc07e6dbfcc6136.png?resizew=121)
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2 . (几何证明选讲选做题)
如图,四边形
内接于圆
,
与圆
相切于点
,
,
为
的中点,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32217457c4e96e2ef155cf15c1b65d97.png)
____________ .
如图,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d5f57a40474205aee752e23ec449d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154ac25c8c8f83e924f5c9f75181f26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fbdef9d23784b3d2c6dda57634e442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32217457c4e96e2ef155cf15c1b65d97.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572037567160320/1572037572378624/STEM/c507f7dd16254564add61d82d32aef5b.png?resizew=173)
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12-13高三上·海南省直辖县级单位·期末
3 . 已知△
内接于⊙
,
为⊙
的切线,
为直线
上一点,过点
作
的平行线交直线
于点
,交直线
于点
.
![](https://img.xkw.com/dksih/QBM/2012/2/16/1570743170301952/1570743176052736/STEM/9d1f0badb2d44529a5cbed434b198e61.png?resizew=248)
(Ⅰ)如图甲,求证:当点
在线段
上时,
;
(Ⅱ)如图乙,当点
在线段
的延长线上时,(Ⅰ)的结论是否仍成立?如果成立,请给予证明;如果不成立,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2012/2/16/1570743170301952/1570743176052736/STEM/9d1f0badb2d44529a5cbed434b198e61.png?resizew=248)
(Ⅰ)如图甲,求证:当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ec004a08fa1e44677983a09cac00d1.png)
(Ⅱ)如图乙,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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10-11高二下·海南·期末
4 . 如图,
切⊙O于点
为
的中点,过点
引割线交⊙O于
、
两点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b1ffac8ffc5f37b96668839083a2b6.png)
![](https://img.xkw.com/dksih/QBM/2011/7/26/1570273735401472/1570273740816384/STEM/8f89c817d214462e9ac15a700a62071f.png)
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11-12高三上·河南洛阳·期末
5 . 选修4-1:几何证明选讲
如图,在△ABC中,∠ABC=90°,以BC为直径的圆O交
![](https://img.xkw.com/dksih/QBM/2011/5/19/1570209865703424/1570209870929920/STEM/0ae9fb78725341509c77d9d9f138fd59.png?resizew=89)
AC于点D,设E为AB的中点.
(1)求证:直线DE为圆O的切线;
(2)设CE交圆O于点F,求证:CD·CA=CF·CE.
如图,在△ABC中,∠ABC=90°,以BC为直径的圆O交
![](https://img.xkw.com/dksih/QBM/2011/5/19/1570209865703424/1570209870929920/STEM/0ae9fb78725341509c77d9d9f138fd59.png?resizew=89)
AC于点D,设E为AB的中点.
(1)求证:直线DE为圆O的切线;
(2)设CE交圆O于点F,求证:CD·CA=CF·CE.
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6 . (几何证明选讲)如图,在
中,
,
,
,以点
为圆心,线段
的长为半径的半圆交
所在直线于点
和
,交线段
于点
,则线段
的长为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d46c17903078e0b38279353c5430d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2011/2/19/1570000250593280/1570000255664128/STEM/adc436f8-0412-490c-87d0-adb467ddb9b5.png)
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