名校
解题方法
1 . 如图,
是边长为2的正三角形,直线
围成一个正三角形
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c42f73b6b4cd5308071e6bedb83049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bbe0491dc037390ef465b4deef4a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d6279b4170c8e4f36488a520ccc49d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 在边长为2的正
中,动点P在以C为圆心且与AB边相切的圆上,满足
.则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734c5f0ab3f244ae2ce1ba7b618cb0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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3 . 如图所示,在单位圆中,
,已知角
的终边与单位圆交于点
,作
,垂足为点M,作
交角
的终边于点T.
(仅用含
的式子表示);
(2)请根据三角形面积公式及扇形面积公式证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8950c7bc835103d52ceffab14b6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f727d47ac94c374adb4fc3131dcca1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a69f6a208dd6671c46271b78430d79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9f3e09dd4b1239622c643d1c33bbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff1dd2db6f898d70a9adef9a0f2ffad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
(2)请根据三角形面积公式及扇形面积公式证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663eb54dde68905674254147ec8397ee.png)
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4 . 设向量
,
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a221e20e74e70f63c8359e7a55206e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ac02c7ecd1af99923002f241a3e3c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf65455b3a39cf6cd951692a1cf9215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423dc529c0baf59600aea1e07acb300f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 给出以下三个件:①
,②
,③
.请从这三个条件中任选一个将下面的题目补充完整,并求解.已知在锐角
中,内角
的对边分别为
且______.
(1)求边长
;
(2)若
的面积
,求角
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bec3032327fbc64700c63463dbcd87f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8770fea557df4d2e7dae279e1ea7ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4edcaf3e729175abc25381bbac394c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
(1)求边长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07abc09e1f0bf5eb87259e3381b3316a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
6 . 五一假期,某景点为了给游客提供便利,在广场大屏幕上滚动播放景区的实时动态信息,已知大屏幕下端
离地面3.5米,大屏幕高3米,若某位游客眼睛离地面1.5米,则这位在距离大屏幕所在的平面多远,可以获得观看的最佳视野?(最佳视野是指看到屏幕上下夹角的最大值)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.3 | D.2 |
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名校
7 . 2024年是宿州市泗县北部新城建立7周年,泗县县政府始终坚持财力有一分增长,民生有一分改善,全力打造我县民生样板,使寸土寸金的商业用地变身“城市绿肺”,老厂房、旧仓库变身步行道、绿化带等.现有一足够大的老厂房,计划对其改造,规划图如图中五边形
所示,其中
为等腰三角形,且
,计划沿线段BE修建步行道.
(2)现准备将
区域建为绿化带且
,当绿化带的周长最大时,求该绿化带的周长与面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd86b47245f0241c3d9f9d375b0c1fa9.png)
(2)现准备将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e17448631d54ca9409ba02b9dc24d3.png)
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名校
8 . 在
中,内角
所对的边分别是
,
,
,已知
.
(1)若
,且
为锐角三角形,求
的周长的取值范围;
(2)若
,且外接圆半径为2,圆心为
,
为圆
上的一动点,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20be9adeb5574fdd3d975f053062887c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988b7e964e313579ab8869d67d5be007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
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名校
解题方法
9 . 在
中,中线
和中线
相交于点
,点
在边
上.
(1)若
,证明:点
是边
上靠近点
的四等分点;
(2)证明:
;
(3)若
,求
中最大角与最小角的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1c0fcbcbbbbcdb0878b63210a839c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126b0abd82f8c42add560f2c7b98e593.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbde778eea12ba7f606e4d9e52242fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
10 . 在锐角
中,三个内角A,B,C所对的边分别为a,b,c,且
,则
的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf1646f0f48ce22e33a36c79abec956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
您最近一年使用:0次