1 . 如图,在△ABC中,
,
,
,直线FM交AE于点G,直线MC交AE于点N,若△MNG是边长为1的等边三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8380348b1978556a8f55d58a58adcbe7.png)
___________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/049d8d5b-b8f4-44fd-a989-ec69e6d92bbc.png?resizew=199)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed8ca6318993a47d7214f0632a40935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5749a9cf79cf78e57fcaaa1b3ff1acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538430485ba05653495cfd10576768db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8380348b1978556a8f55d58a58adcbe7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/049d8d5b-b8f4-44fd-a989-ec69e6d92bbc.png?resizew=199)
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2 . 下列说法正确的是( )
A.在![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() |
您最近一年使用:0次
2021-08-26更新
|
844次组卷
|
5卷引用:浙江大学附属中学丁兰校区2021-2022学年高二上学期期末数学试题
名校
解题方法
3 . 我国著名数学家华罗庚曾说过:“数缺形时少直观,形少数时难入微,数形结合百般好,隔离分家万事休”.数学中,数和形是两个最主要的研究对象,它们之间有着十分密切的联系,在一定条件下,数和形之间可以相互转化,相互渗透.而向量正是数与形“沟通的桥梁”.在
中,试解决以下问题:
于点
.
(i)记
,请用
表示
;
(ii)
,求
的最小值.
(2)已知点O是
的________,且
,求
.
请从下面两个条件中选一个填在上述横线上,并完成解答.(注意:如果选择多个条件分别解答,则按第一个解答计分)
①外心(三条垂直平分线的交点);②垂心(三条高的交点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(i)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d759efa8394237b330b99e220e0174e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a838d9d01d18ed8cfb34d302cd74c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670f6533aaf27dd575f4f26e0c5928d9.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3d786403d56822ee8b5fea39c0941f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4a7a7b5944c122af3ed4379c2de229.png)
(2)已知点O是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b4eb27553163b22b2799e3e7864261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5cb63aeea0b37799404c8fec092b21d.png)
请从下面两个条件中选一个填在上述横线上,并完成解答.(注意:如果选择多个条件分别解答,则按第一个解答计分)
①外心(三条垂直平分线的交点);②垂心(三条高的交点).
您最近一年使用:0次
2022-04-25更新
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576次组卷
|
6卷引用:河南省洛阳市2021-2022学年高一下学期期中数学试题
名校
解题方法
4 . 在
中,
.
为
的重心,试用
、
表示
;
(2)如图2,若点
在以
为圆心,
为半径的圆弧
上运动(包含
、
两个端点),且
,设
,求
的取值范围;
(3)如图3,若点
为
外接圆的圆心,设
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259414bba09b088ca98ed4c3fcee8197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f654198c1e01d97f1378b35d7c68ca.png)
(2)如图2,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b631cd7917b0ac877f875e26c2b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
(3)如图3,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d04286510bedf469f1a53160b21c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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2021-07-19更新
|
730次组卷
|
6卷引用:上海市奉贤中学2021-2022学年高一下学期5月月考数学试题
名校
5 . 在△ABC中,
,F是AC的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3906093705a041d34a663bde830d40da.png)
A.若![]() ![]() |
B.若E是AB的中点,BF与CE相交于点Q,则![]() |
C.若点P在线段AC上,则![]() ![]() |
D.若E是线段AB上一动点,则![]() |
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2022-07-18更新
|
459次组卷
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2卷引用:福建省莆田市2021-2022学年高一下学期期末数学试题
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6 . 关于平面向量,下列说法正确的是( )
A.若![]() ![]() ![]() |
B.已知![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2021-08-07更新
|
689次组卷
|
2卷引用:山东省临沂第一中学2021-2022学年高一下学期6月月考数学试题
7 . 已知
是平面内不共线的三点,点
满足
为实常数,现有下述两个命题:(1)当
时,满足条件的点
存在且是唯一的;(2)当
时,满足条件的点
不存在.则说法正确的一项是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e60a50b78b0f2b5b10b116ce2994b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dc2ba96a19a6426e2ef3944218a9fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c395c97fee9f7ef47b13db57bb80300f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.命题(1)和(2)均为真命题 |
B.命题(1)为真命题,命题(2)为假命题 |
C.命题(1)和(2)均为假命题 |
D.命题(1)为假命题,命题(2)为真命题 |
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解题方法
8 . 如图,在平行四边形ABCD中,BD,AC相交于点O,设向量
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986258300076032/2995511888650240/STEM/9de97c5c-711a-4ef4-bcac-847b592df251.png?resizew=256)
(1)若
,
,
,求证:
;
(2)若点P是平行四边形ABCD所在平面内一点,且满足
,求△ACP与△ACD的面积比;
(3)若
,
,点E,F分别在边AD,CD上,
,
,且
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b54aa2b7f9adf409f0ce8e00615432.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986258300076032/2995511888650240/STEM/9de97c5c-711a-4ef4-bcac-847b592df251.png?resizew=256)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82d16399c8b393539c774d06f410cbe.png)
(2)若点P是平行四边形ABCD所在平面内一点,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfcc49ef13196d82c91f1291b436616a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55881285c3bea9e25144254cf2037540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da346525c48808ae3dca8a05e4408b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec945b565730ef11fe66334927dede1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc29cb1d0b8ca9c4d6286c892952653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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解题方法
9 . 已知M,P,N是平面上不同的三点,点A是此平面上任意一点,则“M,P,N三点共线”的充要条件是“存在实数
,使得
”.此结论往往称为向量的爪子模型.
(1)给出这个结论的证明;
(2)在
的边
、
上分别取点E、F,使
,
,连结
、
交于点G.设
,
.利用上述结论,求出用
、
表示向量
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba27da4302c066fa4cf802ef5829b90.png)
(1)给出这个结论的证明;
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12936b86da4c79d7705b233baa336ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b80c5888abb4ac33ae0ec9d834a9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d82dcb8d9047d6769989282c53b08e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5691149a894127b6dccf09cb340d4247.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/4db1ab520617e340ca2d38b104bd3598.png)
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解题方法
10 . 在平面直角坐标系
中,
是直线
与曲线
在第一象限的交点,
是直线
上的一点,且满足
.
为曲线
上动点,当
取最小值时,
的横坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2fa89a25879322c4cb884763b79104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4f415ebe14b7a5b4fbc3f86393d887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7937ef6b4a2b4d25dc8bbd6c50ba25.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/b9155e905785b48d3a58fabd03e2ed04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次