1 . 已知圆
:
上的点
关于点
的对称点为
,记
的轨迹为
.
(1)求
的轨迹方程;
(2)设过点
的直线
与
交于
,
两点,试问:是否存在直线
,使以
为直径的圆经过原点?若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae760be8ca33cea38a44d790fbd78cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cd70eb2e93cafd9aa2a8b828044d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2 . (选修4-1:几何证明选讲)如图,
是圆
的直径,
,
为圆
上的点,
是
的角平分线,
与圆
切于点
且交
的延长线于点
,
,垂足为点
,若圆
的半径为1,
,则![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/d2947fe9e6024f20b15951dac51e0253.png?resizew=76)
_____ .
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/bb121e6c2b33471590ee57c58f54db33.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/5cdeda5bf2a44e4da9930b74832f52e4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/b5b735a255c942a68849d31b03921028.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/084fd9de96734aa1883b1e561a462891.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/5cdeda5bf2a44e4da9930b74832f52e4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/82011d940d8742438191125312dc4a9d.png?resizew=25)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/bf2f71012381478f970960b0874d7e7c.png?resizew=48)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/69ad07c9cbe54142adea252e981578ce.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/5cdeda5bf2a44e4da9930b74832f52e4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/b5b735a255c942a68849d31b03921028.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/539f8fbec7d84c5d96b3eca74ec7afe4.png?resizew=28)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/c4fa0736a0254bda9602157787cf0680.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/c4fef0bb0db64be5b62eb98e1083c91f.png?resizew=71)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/b3c00a114eb941309d58a40ce3f085a0.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/5cdeda5bf2a44e4da9930b74832f52e4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/9ce1726bf1e5453892d88daf58a379b7.png?resizew=84)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/d2947fe9e6024f20b15951dac51e0253.png?resizew=76)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572042099597312/1572042105487360/STEM/6842c426cb3746249ea99a113123e988.png?resizew=141)
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3 . 选修4﹣1:几何证明选讲
如图,已知PA是⊙O的切线,A是切点,直线PO交⊙O于B、C两点,D是OC的中点,连接AD并延长交⊙O于点E,若PA=2
,∠APB=30°.
![](https://img.xkw.com/dksih/QBM/2016/10/18/1573078232383488/1573078238445568/STEM/68001373d0e44c26a1259b1bff31d3ea.png)
(Ⅰ)求∠AEC的大小;
(Ⅱ)求AE的长.
如图,已知PA是⊙O的切线,A是切点,直线PO交⊙O于B、C两点,D是OC的中点,连接AD并延长交⊙O于点E,若PA=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/2016/10/18/1573078232383488/1573078238445568/STEM/68001373d0e44c26a1259b1bff31d3ea.png)
(Ⅰ)求∠AEC的大小;
(Ⅱ)求AE的长.
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