名校
1 . 如图,四边形
内接于圆
,弧
与弧
长度相等,过
点的切线交
的延长线于
点.求证:
.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce9a5842125844c78436fde416e2145.png)
![](https://img.xkw.com/dksih/QBM/2020/3/31/2431484853633024/2432207860449280/STEM/d7e7dc31b05d401aa392788f605f29c9.png?resizew=129)
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2 . 已知Rt△ABC中,CD是斜边AB上的高,BE是角平分线并且与CD交于F,CH⊥EF,垂足为H,延长CH与AB交于G.
![](https://img.xkw.com/dksih/QBM/2019/4/11/2180013395902464/2181526744260609/STEM/f6e41111c6ee45219076d0203b7050e1.png?resizew=265)
(1)求证:
;
(2)若AC=2BC,求证EA=5FD.
![](https://img.xkw.com/dksih/QBM/2019/4/11/2180013395902464/2181526744260609/STEM/f6e41111c6ee45219076d0203b7050e1.png?resizew=265)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de0f9cba1248d3dd476fd1c6f0afe6d.png)
(2)若AC=2BC,求证EA=5FD.
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3 . 【选做题】
A.[选修4-1:几何证明选讲]
如图,四边形
是圆的内接四边形,
,
的延长线交
的延长线于点
.
求证:
平分
.
![](https://img.xkw.com/dksih/QBM/2017/9/13/1773329033740288/1774103844569088/STEM/dd7af442660d43aba8b4a42ee7fae441.png?resizew=215)
B.[选修4-2:矩阵与变换]
已知变换
:
,试写出变换
对应的矩阵
,并求出其逆矩阵
.
C.[选修4-4:坐标系与参数方程]
在平面直角坐标系
中,已知直线
的参数方程为
(
为参数),曲线
的参数方程为
(
为参数).若直线
与曲线
相交于
两点,求线段
的长.
D.[选修4-5:不等式选讲]
设
均为正数,且
,求证:
.
A.[选修4-1:几何证明选讲]
如图,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb67f27bcda7681b19239a199b4c4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36ff76f9f1ee12db562cde7a58b8c3.png)
![](https://img.xkw.com/dksih/QBM/2017/9/13/1773329033740288/1774103844569088/STEM/dd7af442660d43aba8b4a42ee7fae441.png?resizew=215)
B.[选修4-2:矩阵与变换]
已知变换
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42d846ba2d91e4f5afea23405f65e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
C.[选修4-4:坐标系与参数方程]
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a13b9da94376f8181dc80b2938b7128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c969e381b4ce87b1b545c9b51e0af369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
D.[选修4-5:不等式选讲]
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ab55b69404fdbda2a9e7591ac4f309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469c1bcced970adb1e27bdc365852966.png)
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4 . [选修4-1:几何证明选讲]
如图,已知凸四边形
的顶点在一个圆周上,另一个圆的圆心
在
上,且与四边形
的其余三边相切.点
在边
上,且
.
求证:
,
,
,
四点共圆.
如图,已知凸四边形
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30e50e094cd2849e38859b36aad0b0c.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2017/2/3/1619477902778368/1619477903532032/STEM/5cb641e06fd34edeba2a92b40698fc1b.png)
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5 . A.如图所示,
是园
内两条弦
和
的交点,过
延长线上一点
作圆
的切线
,
为切点,已知
求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42453c833ec3a7ce4872fec650cd9d7.png)
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946591010816/STEM/56225fe9c4bc4c679860b36e94307e77.png?resizew=183)
B.已知矩阵
,
.求矩阵
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e08ea53af50d2e51b060f21d22d17f4.png)
C.在平面直角坐标系
中,直线
的参数方程为
(
为参数),以坐标原点
为极点,
轴正半轴为极轴的极坐标系中,曲线
的极坐标方程为
,已知直线
与曲线
相交于
两点,求线段
的长.
D.已知
都是正数,且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff89d2ee12c1cd886422896208f44fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42453c833ec3a7ce4872fec650cd9d7.png)
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946591010816/STEM/56225fe9c4bc4c679860b36e94307e77.png?resizew=183)
B.已知矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad34e36c307e8ca0a490adfd34566a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05593a9391c462e0e2538844f78e3b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e4cddb450523d6ab69b9080aeb0d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8fa78398b62e6805404f020a0d00e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e08ea53af50d2e51b060f21d22d17f4.png)
C.在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37686fd77607f96d259cfd117c863bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bddf0b3db29426b5f1c396736b7f667.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
D.已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2edfccf9159bb4010669e938f788149b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dcbfa0d3655f4c20db4363f69e6c36.png)
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6 . 选修4—1:几何证明选讲
如图,
是⊙
的直径,
是⊙
上的两点,
⊥
,过点
作⊙
的切线FD交
的延长线于点
.连结
交
于点
.
求证:
.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9aa3f533894ca87a394f7a1dfd0ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768c46a01f0f3403b7bb59348ca28823.png)
![](https://img.xkw.com/dksih/QBM/2015/1/7/1571957203386368/1571957209137152/STEM/0d9d65d4329041bc8860544ed9104ad5.png)
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