2024高三·全国·专题练习
1 . 已知点O为△ABC外接圆的圆心,且
,则△ABC的内角A=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6d8be63c22a97f160e69f6810d2595.png)
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2 .
中,
,点
是
内切圆
上一点,且
,则
的最小值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4290bd7630dd33c70f0defb7cb7d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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3 . 窗,古时亦称为牖,它伴随着建筑的起源而出现,在中国建筑文化中是一种独具文化意蕴和审美魅力的重要建筑构件.如图是某古代建筑群的窗户设计图,窗户的轮廓ABCD是边长为50cm的正方形,它是由四个全等的直角三角形和一个边长为10cm的小正方形EFGH拼接而成,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec51d22434c8081b7c9acfc3980dbf8e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec51d22434c8081b7c9acfc3980dbf8e.png)
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4 . 已知向量
满足
,
与
的夹角为
,则当实数
变化时,
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fa8ea29001bb1f0c1e5157aff2fca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fdd453a7bf9249f37924848b85727d.png)
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5 . 大约在公元222年,赵爽为《周髀算经》一书作注时介绍了“勾股圆方图”,即“赵爽弦图”.如图是某同学绘制的赵爽弦图,其中四边形
均为正方形,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33639898cef2ce955a8f3b45659ad1c7.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f188ef0f40d8225e1838cdd34832a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59bc3943c9bc08400c3751b31c7ce00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33639898cef2ce955a8f3b45659ad1c7.png)
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2024-03-27更新
|
667次组卷
|
2卷引用:河南省濮阳市2024届高三下学期第一次模拟考试数学试题
2024高三·全国·专题练习
解题方法
6 . 若点
在以
为圆心,6为半径的弧
上,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8510ba07bd64dd7bcc654f3c47e9ddc.png)
,则
的取值范围为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d5bb3031d527aa204fcbfb5de0f34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8510ba07bd64dd7bcc654f3c47e9ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7181d80909ae5c8186f0ef38f9bbf62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6f3c30a6691c86db14441bd51d777d.png)
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7 . 正方形
的边长为
,
是
的中点,
是
边上靠近点
的三等分点,
与
交于点
,则
的余弦值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3b8144f5664421e3c2d3cff9e5e483.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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9 . 已知
是同一平面上的3个向量,满足
,且向量
与
的夹角为
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c71ddc7c848789bd46e341bb5fa6316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015804533449e04f3e4f9f2d54326f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222fd0837d18068c2471dac135e79f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83634e314df24df73ae37d25a44d20e3.png)
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10 . 等边
的边长为2,三角形
所在平面内有一动点
,满足
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ae300e4ff3e89d0e1e5671eacd9585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811f2b0933367b7cb32a7696510f2089.png)
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2024-03-24更新
|
591次组卷
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2卷引用:云南省昆明市第一中学西山学校2023-2024学年高一下学期3月月考数学试卷