解题方法
1 . 如图,动点C在以AB为直径的半圆O上(异于A,B),
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ea4321e821c1e78e311fcd37cf6465.png)
______ ;
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51b89f545616ef48f3706850107ad95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f213621229843639780aae87fa29584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56387ff53874620addcb0b91a605a309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ea4321e821c1e78e311fcd37cf6465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7906b66906ec5943b3bbd9ce9a47e7.png)
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解题方法
2 . 在平行四边形
中,
,
,点
在边
上,满足
,则向量
在向量
上的投影向量为________ (请用
表示);若
,点
,
分别为线段
,
上的动点,满足
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4814565292192e40bd86a10ee7b661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5dc30c658a62dbd19edf9e0bc10e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dae942a35d9c35f196959a35dc608e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12529b9d6f852fa8ff21ea95e0591c0c.png)
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解题方法
3 . 已知
中,
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808382ba1d893826a026d85e0cd67609.png)
_________ ;若
,当
最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c95c6fedd33a4a8b2d25c4a2bd8d077.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dfe8aa4868de1181b5263f7a1ed995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0877d52e0b256d24f1877c4f1d3dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d9e6ae2b22b22796fc2b4a648ae65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808382ba1d893826a026d85e0cd67609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2b622913dfd7d0c099db3bdfed61d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c95c6fedd33a4a8b2d25c4a2bd8d077.png)
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4 . 已知在矩形
中,
,
,动点
在以点
为圆心且与
相切的圆上,则
的最大值为___________ ;若
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb420defc29953c389e10bc28f9a4c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046fd6053b22ad79fcd9f4ad0e58352b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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5 . 已知
是半径为2的圆上三个动点,①若
,则
的最大值为__________ ,②若
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b48e12bab152aeb25ee855bd60b403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1bf2961df6e0fbfac146c634a0992d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
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解题方法
6 . 河中水流自西向东流速为
,小船自南岸
点出发,想要沿直线驶向正北岸的
点,并使它的实际速度达到每小时
,该小船行驶的方向为______ ,小船在静水中的速度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d455d27d3d20ae94b9cece9651777a.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/ddb720f3c60d75ca530492930aad0e6c.png)
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7 . 已知正六边形ABCDEF的边长为1,若点H是正六边形ABCDEF内或其边界上的一点,则
的最小值为______ ;若点N为线段AE(含端点)上的动点,且满足
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76425c16d41a92260a6cdcb11b2b869e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8dfaaebbeea40bce3f96d8bc1719f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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8 . 青花瓷,常简称青花,代表了我国古代劳动人民智慧的结晶,是中国瓷器的主流品种之一.图一是一个由波涛纹和葡萄纹构成的正六边形青花瓷盘,已知图二中正六边形的边长为
,圆
的圆心为正六边形的中心,半径为
,若点
在正六边形的边上运动,动点
在圆
上运动且关于圆心
对称.(i)请用
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfd72e67dcfcc2578d4612ce1a6ad.png)
_______ ;(ii)请写出
的取值范围_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1cdc58c5c894ccf294e6f1fa18aae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfd72e67dcfcc2578d4612ce1a6ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
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2024高一下·全国·专题练习
9 . 某人从点
向正东方向走30 m到达点
,再向正北方向走
m到达点
,则此人的位移的大小是________ m,方向是北偏东________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48de9da1b7fca16b44d9f6ee454a6c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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解题方法
10 . 如图是六角螺母的横截面,其内圈是半径为1的圆
,外框是以为
中心,边长为2的正六边形
,则
到线段
的距离为__________ ;若
是圆
上的动点,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a302ee9825909922d7c0fa859e8735c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/1918b47c-b7a8-434d-9857-4b0c3dea581a.png?resizew=150)
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