名校
1 . 如图,点
在
外,
为
中点,
在
上,且
,连接
并延长交
于点
,则
能否成立?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a122e25cf4eb9f03ffe5ec823bfc31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f834e8d16a6e26a65ff2ed5809823f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc960c33db841e63ab5983f7a5a847bd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/427d79ea-94e7-4032-9151-d2015cbd61e2.png?resizew=131)
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2 . 点G为
的中点,
,
,
延
翻折使点F落在
上,四边形
为矩形,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b644e2bc1df31ac474d646b1d1319400.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7d2a2da5144f0bf6ce091c56b3d5a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fc998d33cdf37c272f79cfd64b7b99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d480e8b2c516612b47a19cb62d9bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b644e2bc1df31ac474d646b1d1319400.png)
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3 .
可以表示为数轴上1右边的点
(1)
可以在平面直角坐标系中表示为__________;
(2)在坐标系中用阴影表示满足
的点;
(3)
与上述阴影部分围成的封闭图形(不含边界)中包含2个整点(横纵坐标均为整数的点)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecedde061163f1e524308688204e9ef9.png)
(2)在坐标系中用阴影表示满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1be1f7713bf93673b52fef8d8cae01.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4 . (1)已知
为
中点,过点
作
于
,交
于点
,求
.
(2)已知
,过点
作
于
,交
于点
,求
.
(3)在(2)的条件下,
为常数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c4c49765e33742b4204d6904dc3a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5378a3867bf1a7386b1330aa8b36f0a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/1e748517-2524-4763-aeb1-30d7a2bd7e1d.png?resizew=155)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df89cefacfd826262825276a739ca4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5378a3867bf1a7386b1330aa8b36f0a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/7e2e9fd4-ce48-414d-8682-dee6f813a104.png?resizew=154)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03cab451843012fd80fa6cc698c648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe857997fa13837880f520673db7809.png)
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5 . 已知
是圆
的切线,
是直径,
是弧
的中点,
是直线
与
的交点
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/6442f898-647e-4b07-bfd5-6b3db2686872.png?resizew=163)
(1)
,求
;
(2)
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/6442f898-647e-4b07-bfd5-6b3db2686872.png?resizew=163)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9639896487e6cf18e8fd02d2a7ed2087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d9d43e562dd78eeb55b5ed675b6f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b020e3977f31139a1153a1c1d23dc7.png)
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6 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2236f581b11a0bb63addd062529acee8.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d3326ddf0b6bf28a05a7b490563bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2236f581b11a0bb63addd062529acee8.png)
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7 . 如图,
中,
分别在射线
上滑动,开始时,点
与点
重合.当点
向点
运动时,点
沿着
方向运动(保持
形状不变),点
从起始位置运动到点
的过程中,点
的运动轨迹的长度是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88caf684bf220b0dad460d75361bdd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81451aab89c418bd1b7996627b58c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2281b85925f638db0eb6cfe27d0558f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.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/editorImg/2024/2/24/0fd0237a-4b80-4eb7-baa8-67e5a519fbe0.png?resizew=152)
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8 . 函数
图像与
轴交于点
,将函数图像绕点
顺时针方向旋转
后得到的函数图像对应的表达式是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e192225e485cbfc7fedaa57af03798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
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9 . 如图,
为
的外接圆,
为
边上的高.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c8162e02-5e95-46fc-bd52-fb046a22dbe8.png?resizew=159)
(1)请写出
与
半径
的关系;
(2)如果作
的角平分线交
于
,那么
是否是
的角平分线?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c8162e02-5e95-46fc-bd52-fb046a22dbe8.png?resizew=159)
(1)请写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831f65020b4b53186e44d5312d063e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)如果作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a037c23a11c7783b1b44988c21634f.png)
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10 . 将
的线段分成
段,每一段长均为不小于
的整数厘米,分完后,任何三段都不能构成三角形,则
最大为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e651babde701d43faadf589dd4e14c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1d7f842f070363d1134a387aa10e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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