【提出问题】我们知道,点和圆有三种位置关系(如图1).已知在⊙O中,点A、B、C分别是圆外、圆上、圆内的点,点D、E是
上不与点B重合的任意两点,分别连接AD、AE、BD、BE、CD、CE,如何比较
、
、
的大小关系.
【解决问题】小邕利用已学知识判断
和
的大小关系,步骤如下:
解:
,理由如下:
如图2,延长DC与
相交于点F,连接EF,由同弧或等弧所对的圆周角相等,可知
,
∵
是
的外角,
∴
,
∴
,
∴
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/a464b490-6591-40af-a536-0dd7e0561a4e.png?resizew=491)
(1)请参照小邕的解题步骤,比较
和
的大小关系,并说明理由.
【实践应用】
(2)如图3,海边立有两座灯塔A、B,暗礁分布在经过A、B两点的弓形(弓形的弧是⊙O的一部分)区域内,
.为了避免轮船P触礁,轮船P所在的位置与两座灯塔A、B的视角
度数的最大值是多少?并说明理由.
(3)2022卡塔尔世界杯正在如火如荼地进行中,全民足球热情高涨.因此某校举办了足球比赛,在其中一场比赛中(如图4),甲带球奔向对方球门
,当他带球冲到A点时,同伴乙已经冲到B点,同伴丙已经冲到C点.此时有三种射门方式:第一种是甲直接射门;第二种是甲将球传给乙,由乙射门;第三种是甲将球传给丙,由丙射门.仅从射门角度越大,进球概率越大的角度考虑,请直接写出应选择第几种射门方式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccdccf6ca4ab39cc41fe3f7afc2846d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc42c06a556f40877176bb5ada88db95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0de33a4f5fa5d6399c9044c79e9d06.png)
【解决问题】小邕利用已学知识判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc42c06a556f40877176bb5ada88db95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0de33a4f5fa5d6399c9044c79e9d06.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc23bc9bb1c2c4e609ab0560b59030d.png)
如图2,延长DC与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6f0699521576549373a8534627492f.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f147986315177306d616820ce20684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164b3491caa0b74c03bfd6d5893c836f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c1d6cbe32ef4e00b56ceb40d71a7af.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772ebecfc28b17a14dc49843a70c9122.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52e50bafef754cfab861325587ecb00.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/a464b490-6591-40af-a536-0dd7e0561a4e.png?resizew=491)
(1)请参照小邕的解题步骤,比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccdccf6ca4ab39cc41fe3f7afc2846d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc42c06a556f40877176bb5ada88db95.png)
【实践应用】
(2)如图3,海边立有两座灯塔A、B,暗礁分布在经过A、B两点的弓形(弓形的弧是⊙O的一部分)区域内,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fbfaf436cd692fde72f83a265f50de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540b05ed65a4dc86d84e6fe4ec6f6e5e.png)
(3)2022卡塔尔世界杯正在如火如荼地进行中,全民足球热情高涨.因此某校举办了足球比赛,在其中一场比赛中(如图4),甲带球奔向对方球门
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
更新时间:2023-01-03 22:14:05
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【推荐1】如图,AB是⊙O的一条弦,OD⊥AB,垂足为点C,交⊙O于点D,点E在⊙O上.
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(1)若∠AOD=52°,求∠DEB的度数;
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解答题-作图题
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适中
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【推荐2】已知⊙O,请用尺规完成下面作图,不写作法,保留作图痕迹.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/1961ca6e-b110-49ab-ada6-97ffe3e6bc13.png?resizew=190)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/1a3c38f4-4c10-4348-8858-5f76b5be9d39.png?resizew=190)
(1)如图①,在
上作一个45°的圆周角;
(2)如图②,在
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/1961ca6e-b110-49ab-ada6-97ffe3e6bc13.png?resizew=190)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/1a3c38f4-4c10-4348-8858-5f76b5be9d39.png?resizew=190)
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(2)如图②,在
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【推荐1】如图,在四边形
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【推荐2】如图:
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,
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