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解题方法
1 . 古希腊数学家托勒密对凸四边形(凸四边形是指没有角度大于180°的四边形)进行研究,终于有重大发现:任意一凸四边形,两组对边的乘积之和不小于两条对角线的乘积,当且仅当四点共圆时等号成立.且若给定凸四边形的四条边长,四点共圆时四边形的面积最大.根据上述材料 ,解决以下问题,如图,在凸四边形
中,
,
,
,
(图1),求线段
长度的最大值;
(2)若
,
,
(图2),求四边形
面积取得最大值时角
的大小,并求出四边形
面积的最大值;
(3)在满足(2)条件下,若点
是
外接圆上异于
的点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422f54faa21cdabc65b912b0e76eb68e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212bfbd5575772ca36d6fc3e7b246e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c41757ae282475fb29ec1e8e02045d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)在满足(2)条件下,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b94fd6403a7f18702993f80e29bfe1.png)
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3卷引用:辽宁省协作校2023-2024学年高一下学期5月期中考试数学试题
辽宁省协作校2023-2024学年高一下学期5月期中考试数学试题安徽省阜阳市第三中学2023-2024学年高一下学期第二次调研(期中)数学试题(已下线)第9题 解三角形在几何图形中的应用(高一期末每日一题)
2 . 函数
相邻的两个零点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc574389b74c0e846657b2e24ffe115f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd5543f6cc0a25deb6410dd48cce9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d3c0e7508ff7fd36faba07a0aa41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc574389b74c0e846657b2e24ffe115f.png)
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3 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161d39fa1cb0e994941c02bd4ab971b1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8529a52e32b12244bd535641221e83e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161d39fa1cb0e994941c02bd4ab971b1.png)
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4 . 若函数
在
上单调,则
的取值可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c64550e7b3bcf3b8793bf737a9fb75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d6d18a05bace9fa8271eae07020673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a8855aff1b33b5849d88513101d8d8.png)
的部分图像如图所示,
是等腰直角三角形,其中
两点为图像与
轴的交点,
为图像的最高点,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a8855aff1b33b5849d88513101d8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3fa5f9a8d31a4425722a9e5ee2533e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/8d0b5bc0105f55a7fa980ae7b1019d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f6f96a7c67ccb294c6f9d209061c96e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 在
中,角A,B,C所对的边分别为a,b,c,
,
.
(1)求角B的大小;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6129fbf40a950fc8c516f0abaab21957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab2d91c489085219ac31c1ef8d7430f.png)
(1)求角B的大小;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708fb15948f1fc5e6c6838c573bfa4ce.png)
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7 . 在
中,角A,B,C所对的边分别是a,b,c,且________,在①
;②
;③
,这三个条件中任选一个,补充在上面的横线上,并解答下列问题:
(1)求角A的大小;
(2)若AD是
的角平分线,且
,
,求线段AD的长;
(3)若
,判断
的形状.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b6c4e81dcf5e218116edd0962bd42ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e732ded6a7c9edfe2c223eb2e1959f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4683a7d4d99602c8e24c901428235ad.png)
(1)求角A的大小;
(2)若AD是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8018ca74a3562c4a9910a17ab9e37a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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8 . 在复平面内,复数
对应的点关于直线
对称,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95423c449f5d44dd949bf3b0130946f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1ef88d9924ca9e5f0609a039b1ccba.png)
A.![]() | B.5 | C.![]() | D.1 |
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4卷引用:辽宁省东北育才学校高中本部2023-2024学年高一下学期期中考试数学试题
辽宁省东北育才学校高中本部2023-2024学年高一下学期期中考试数学试题(已下线)核心考点4 复数及其运算 B提升卷 (高一期末考试必考的10大核心考点) (已下线)专题06 复数常考题型归类-期末考点大串讲(人教B版2019必修第四册)广东省华南师范大学附属中学2024届高三下学期模拟测试(一)数学试题
名校
解题方法
9 . 已知|
,
,
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c357efba6277c0b5e46cabeb93f7a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b507692d26f6f38f5418a86f2b10d985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bad01658b1ef75f08bc1c28f4bc57f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b847ccdc479d753206a89eb94e37754.png)
A.2 | B.![]() | C.3 | D.4 |
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10 . 已知向量
,
,
,满足
(
),且
,若
为
,
的夹角,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e21027d4c039e83e33f67cef3e82461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffe803ace64d7cc9e7179712a7ff373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:辽宁省实验中学2023-2024学年高一下学期期中阶段测试数学试卷
辽宁省实验中学2023-2024学年高一下学期期中阶段测试数学试卷河南省安阳市林州市第一中学2023-2024学年高一下学期5月月考数学试题(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)