1 . 如图,在矩形
中,
,点P从C点出发,沿
方向运动至B点(不与点B重合),连接
,过点P作
交
于Q,以
为斜边作直角三角形
,且
,O为直角顶点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/4dd7f3b8-0294-4f1e-a568-e4194ad8e5ea.png?resizew=184)
(1)在点P的运动过程中,求
的外心到
边的距离最大值;
(2)当点P从C点运动至点O恰好落在
上时,求点O的运动路径长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55df42b1f17bb4f913fd954e599b129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da965e50519eac2d0a7c81a464121c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161ea3eaa2e28747507c1c0e4a7b39f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3043d7cac94429fcb1b053a2909282.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/4dd7f3b8-0294-4f1e-a568-e4194ad8e5ea.png?resizew=184)
(1)在点P的运动过程中,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当点P从C点运动至点O恰好落在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2 . 《几何原本》卷2的几何代数法(以几何方法研究代数问题)成了后世西方数学家处理问题的重要依据,利用这一方法,很多代数的公理或定理都能够通过图形实现证明.现有如图所示图形,点F在半圆O上,且
,点C在线段OB上.设
,
.结合该图形解答以下问题:
![](https://img.xkw.com/dksih/QBM/2022/10/5/3081057399521280/3083291043676160/STEM/be658cc3080d48dfbe97e30855978e09.png?resizew=168)
(1)用a,b表示OF,OC,FC;
(2)根据OF与FC的大小关系,结合(1)的结论可得到什么不等式?并证明
是该不等式取等号的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebef5bab02280cdc99cc7f689135cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3d296e0d7154a170cb7d3ae42989b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a88b719166fcc1431f876bc8c5656c.png)
![](https://img.xkw.com/dksih/QBM/2022/10/5/3081057399521280/3083291043676160/STEM/be658cc3080d48dfbe97e30855978e09.png?resizew=168)
(1)用a,b表示OF,OC,FC;
(2)根据OF与FC的大小关系,结合(1)的结论可得到什么不等式?并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
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2022-10-08更新
|
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3 . 如图,抛物线
的对称轴为直线
,且抛物线经过
,
两点,交x轴于另一点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/24e534a9-5356-4a44-b087-8e0b9d0e5821.png?resizew=420)
(1)求抛物线的解析式;
(2)过点A作直线
的垂线交y轴于点D,平移直线
交抛物线于点E,F两点,连结
,
.若
为以
为斜边的直角三角形,求平移后的直线的解析式.
(3)设对称轴直线
与x轴交于M,点P为抛物线上对称轴左侧一点,直线
交抛物线于另一点Q,点P关于抛物线对称轴对称点H,直线
交抛物线对称轴于G点,在点P运动过程中
长是否为一定值,若为定值,请求出其值,若不为定值,请求出其变化范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a998a12fe8eaedcb5880790be542d258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c98a7f3a8bf384b1dfc1d34aebd46d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcf82d01c39fd2c96e1edba0ad37dd6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/24e534a9-5356-4a44-b087-8e0b9d0e5821.png?resizew=420)
(1)求抛物线的解析式;
(2)过点A作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90c780dac29ff8b7df5881d3b33abab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecff6005f926665a926c07ad62e0f032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd1c4e883518a7ac5a7517615e47e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)设对称轴直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c98a7f3a8bf384b1dfc1d34aebd46d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c018b37259f3ead2ab2d94bd744f44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e953a4a5f98c96bbe67cbaadf76d9.png)
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2022-09-28更新
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4 . 二次三项式
因式分解正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dbfffbe6cf454b0a89d5eadbee1e8ed.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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