1 . 如图,在
中,
为
边上的高线.
为三角形内一点,由
向三角形三边作垂线,垂足分别为
,
,
,已知
,
,
,
依次构成公差为1的等差数列.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/b3b5eae2-36c0-4719-b27a-c137e5ebc98e.png?resizew=200)
(1)求
的面积;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa8299316c747f7e8c54ee2b073a17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9e36c5987d6730e846753e0552c7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c178c9abab25de6a69a3d5b98c55bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/b3b5eae2-36c0-4719-b27a-c137e5ebc98e.png?resizew=200)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fce32bd941595be3880d48c16e0495.png)
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2 . 已知抛物线x2=2py(p>0)上一点R(m,2)到它的准线的距离为3.若点A,B,C分别在抛物线上,且点A、C在y轴右侧,点B在y轴左侧,△ABC的重心G在y轴上,直线AB交y轴于点M且满足3|AM|<2|BM|,直线BC交y轴于点N.记△ABC,△AMG,△CNG的面积分别为S1,S2,S3.
(2)求
的取值范围.
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf9db375bb55a6b1edc8bc05a2fb99c.png)
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2020-03-19更新
|
1492次组卷
|
4卷引用:2020届浙江省名校协作体高三下学期3月第二次联考数学试题
2020届浙江省名校协作体高三下学期3月第二次联考数学试题浙江省宁波市北仑中学2021-2022学年高二上学期期中数学试题(已下线)第三章 圆锥曲线的方程(A卷·知识通关练)(5)宁夏银川一中、云南省昆明一中2024届高三下学期5月联合考试二模理科数学试卷
名校
3 . 如图,直线
,点
是
之间的一个定点,过点
的直线
垂直于直线
,
(
为常数),点
分别为
上的动点,已知
.设
(
).
![](https://img.xkw.com/dksih/QBM/2020/1/30/2388072192073728/2388181329387520/STEM/259f8d3625d64876909c2ad47f08f89a.png?resizew=186)
(1)求
面积
关于角
的函数解析式
;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f419750fe2e81297e21646268adb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da24c3c749a2daba3d3a5136c16fdb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50515b0461f55861fd28f2774a2f01dc.png)
![](https://img.xkw.com/dksih/QBM/2020/1/30/2388072192073728/2388181329387520/STEM/259f8d3625d64876909c2ad47f08f89a.png?resizew=186)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8135ce2fc33a303efd2087106709d44e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8135ce2fc33a303efd2087106709d44e.png)
您最近一年使用:0次
2020-01-30更新
|
1100次组卷
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7卷引用:江苏省无锡市2019-2020学年高一上学期期末数学试题
4 . 如图,在四面体
中,G是BC的中点,E,F满足
,
,设平面
交
于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d815e0eb03562b95f1f92f98b8a5eb7a.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ec642018e5dee22d061d144ef86391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca527662b704bef1bf8c8997fb3a234e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0df705957958cc7af0766a41eebce6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d815e0eb03562b95f1f92f98b8a5eb7a.png)
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445374804426752/2445519356231680/STEM/4e6d65a4-0c61-407d-9810-ad0efea230b3.png)
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5 . 已知
的面积等于1,若
,则当这个三角形的三条高的乘积取最大值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e3fc39d2b508cc1cae769a5e7266c0.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e3fc39d2b508cc1cae769a5e7266c0.png)
您最近一年使用:0次
2019-09-18更新
|
4491次组卷
|
11卷引用:2020年1月中学生标准学术能力诊断性测试诊断性测试理科数学试卷
2020年1月中学生标准学术能力诊断性测试诊断性测试理科数学试卷中学生标准学术能力诊断性测试2019-2020学年高三1月(一卷)数学(理)试题(已下线)专题01 少丢分题目强化卷(第二篇)-备战2021年新高考数学分层强化训练(北京专版)重庆市2021届高三上学期第二次预测性考试数学试题浙江省名校协作体2019-2020学年高三第一学期第一次联考数学试题(已下线)专题4-2 正余弦定理与解三角形小题归类1-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)四川省泸州市泸县第四中学2022届高三三诊模拟考试理科数学试题(已下线)必刷卷01 (理)-2022年高考数学考前信息必刷卷(全国乙卷)苏教版(2019) 必修第二册 必杀技 第11章 解三角形 11.2 正弦定理 第11.2 节综合训练黑龙江省鹤岗市第一中学2022-2023学年高一下学期期中数学试题(已下线)专题19 解三角形中的面积问题
名校
6 . 曲线
在点
处的切线与坐标轴围成的三角形的面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c185529266ee05b4ac0c6c6c8c2ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d25e70d37af93796965efc8d342185.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-12-21更新
|
600次组卷
|
2卷引用:山西省朔州市怀仁县第一中学2018-2019学年高二下学期期中数学(文)试题
7 . 如图所示,在直角
中有一内接正方形
,它的一条边
在直角
的斜边
上,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3efd363abedb20d3c8d395e7ed11c681.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/603cacbe-5162-4232-8cba-15e0366989d7.png?resizew=189)
(1)用
和
表示出
的面积
和正方形
的面积
;
(2)当
变化时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3efd363abedb20d3c8d395e7ed11c681.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/603cacbe-5162-4232-8cba-15e0366989d7.png?resizew=189)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92cd169360ffdb827d40f3dbc7c7ad1.png)
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8 . 在直角坐标平面上,若一个过原点且半径为r的圆完全落在区域
内,则r的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593e8604cf62293dab71402b3ab94b3e.png)
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9 . 在△ABC中,已知
,设0为△ABC的内心,且
.则λ+μ=________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751365882078f83f46e0a3a772393506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d46574732ca9040b5b76c76e7e06fe.png)
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2018高三·黑龙江·竞赛
名校
10 .
中,
,C所对的边分别为
,
.
(1)求
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0ae8e92dd3119d41f2c830ea526516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ace74bfb716753490ebe0e740ff5baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2060b4b87b84ef46a38566d7954596.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c0a6efe18abe173b91498ff750cd62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd8dc7ac339df242fa74391768120ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377d8f968709442464168c01380441e8.png)
您最近一年使用:0次
2019-01-28更新
|
320次组卷
|
4卷引用:2018年全国高中数学联赛黑龙江省预赛