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1 . 在平面直角坐标系xOy中,已知P是圆C:
上的动点,若
,
,
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37f1a3fd7e442103c95e3ac8623fe7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dbad6b8e9062364691018424fe7df7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9bce61b0385ba876f309356017b2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3236613835e42ebb143c1ff3a1c75e1.png)
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2 . 已知平面向量
满足:
,若
,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fddc1f1c50aab4de7fff286d691b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612dbe580ca825f9a003fc3ee2d811a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de1132049be5728e32cbb0771917a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5382bd3fda4371289ce6800f71f9565.png)
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2024-04-08更新
|
818次组卷
|
3卷引用:2024届上海市长宁区高三下学期二模数学试卷
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3 . 已知等边
的外接圆
的面积为
,动点
在圆
上,若
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4d9a7c9b2ee0253a3a11d5117f9f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df2c3aefa325943bcd20a48b28e9251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-04-05更新
|
2085次组卷
|
5卷引用:华大新高考联盟2024届高三4月教学质量测评理科数学试题(老教材全国卷)
2024高三·全国·专题练习
4 . 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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5 . 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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6 . 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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fdd453a7bf9249f37924848b85727d.png)
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7 . 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
|
669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
8 . 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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9 . 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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10 . 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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