解题方法
1 . 赵爽是我国古代数学家,大约在公元222年,他为《周髀算经》一书作序时,介绍了“勾股圆方图”,亦称“赵爽弦图”.(以弦为边长得到的正方形由4个全等的直角三角形再加上中间的一个小正方形组成,如图①),类比“赵爽弦图”,可构造如图②所示的图形,它是由3个全等的三角形与中间一个小等边三角形拼成的一个较大的等边三角形,其中
,则
的值为______ ;设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bbe0491dc037390ef465b4deef4a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412e959d8e97ae6bee534a319662e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e507d3941363e9dbeac8be35134727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
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解题方法
2 . 如图,在边长为1的正方形ABCD中,点P是线段AD上的一点,点M,N分别为线段PB,PC上的动点,且
,
(
,
),点O,G分别为线段BC,MN的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6c3cb44e29fa620a90b35a5cfed0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d44c0b033ff6b8d35f98eeb1a91b979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ce87a89977ef116559a150dd517d17.png)
A.![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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3卷引用:山西省太原师范学院附属中学等2023-2024学年高一下学期5月质量检测数学试卷
山西省太原师范学院附属中学等2023-2024学年高一下学期5月质量检测数学试卷湖北省黄冈市浠水县第一中学2023-2024学年高一下学期期末质量检测数学试题(已下线)【高一模块一】难度3 小题强化限时晋级练(基础3)
解题方法
3 . 如图,在
中,已知
,
,
,
,点
为
边的中点,
,
相交于点
.
;
(2)求
.
(3)用
和
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348216467fda035329fe8fac46b39911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecb91d19a693299dcdad4059b6237a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f580d157cf3e3b90c4c11a36e8fb467c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51dafedc6530144f32cf56c2f56a3413.png)
(3)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
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解题方法
4 . 在
中,
.
为边
上一点,
为边
上一点,
交
于
.
(1)若
,求
;
(2)若
,求
和
的面积之差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb9a326aece050cf5e9f4713176bb1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b210112e06c09e01255f901f22417500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abf471da32c43bc2e56679a2038cac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c444af7a40000c15940578f9826ef99.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b0216fb4161cda4be672d5224cedfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbd6b9f85c086ac95562fe45e8d969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f483a71f250bac98cb05d67dccad14.png)
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2卷引用:福建省厦门第一中学2023-2024学年高一下学期6月适应性练习数学试卷
名校
解题方法
5 . 如图所示,在边长为3的等边三角形
中,
,且点P在以
的中点O为圆心、
为半径的半圆上,若
,则下列说法正确的是____________ .
①
②
的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb03865bc5bbd5acdf68260d6a1454f6.png)
③
最大值为9 ④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de75a2e98f7c16a0be0ccbb8fd4b72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81889370d45239939a36de53c4445d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95d146bdcc8ac0a256c12696e9b9826.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc5c4b886a48affa3e6103f7e4c2bfd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb03865bc5bbd5acdf68260d6a1454f6.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ccdceb57c6df84b42b1b9032a636e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de75a2e98f7c16a0be0ccbb8fd4b72b.png)
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解题方法
6 . 如图,设
中角A,B,C所对的边分别为
为
边上的中线,已知
且
.
的面积;
(2)设点
,
分别为边
上的动点,线段
交
于
,且
的面积为
面积的一半,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97598771e2f206cd08b11e552121490b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55ca16acc058af4ae6a87ddd6c55234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)设点
![](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/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e26b3b7e7293a85fa650b57cedba871.png)
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解题方法
7 . 已知O为
的内心,角A为锐角,
,若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f4d0c14825958104860b736876cb74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bce82dca9408bbaa708c6d490430af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19bc9c7083b1e9538337a3038712896.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . “奔驰定理”因其几何表示酷似奔驰车的标志而来,是平面向量中一个非常优美的结论,奔驰定理与三角形的四心(重心、内心、外心、垂心)有着美丽的邂逅.它的具体内容是:如图,若
是
内一点,
的面积分别为
,则有
.已知
为
的内心,且
,若
,则
的最大值为__________ .
![](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/7c06b7d20cc3e6b13af9fe40fc3faf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccb3de366206f32e0c9045e63b2e205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b129e8572f675627f5a7a2f782413f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dcb984f7275b7047dbbd4c000e22b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dfa5c97db56ae183a823782432cb3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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4卷引用:湖南省名校联考联合体2023-2024学年高一下学期期中考试数学试题
湖南省名校联考联合体2023-2024学年高一下学期期中考试数学试题(已下线)【讲】专题五 平面向量的综合问题(压轴大全)(已下线)【练】 专题六 平面向量与三角形四心问题(压轴大全)云南省保山市智源高级中学2023-2024学年高一下学期第二次(6月)月考数学试题
名校
解题方法
9 . 在
中,
,
,
.点
为
所在平面上一点,满足
(
、
且
).
(1)若
,用
,
表示
;
(2)若点
为
的外心,求
、
的值;
(3)若点
在
的角平分线上,当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d81d732204a3c2384a27606f858677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec7ea9a9bf46fe5dfe7bdb028289bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3276b5e12396fc4753eb3f8254f9fa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d100f6eb4bfc0b0191c12d5ab35d0d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03698c9b972ce8c2a569195d00d0312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbaeae7045ad94158cdf5ae97073bc17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34bf00aeba15bce2cdee8ab487388dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ce17f8f08bc11bd78885c80223466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21306b0138363c1cb99ee8c1ecc5a486.png)
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解题方法
10 . 在正三棱柱
中
,
的重心为
,以
为球心的球与平面
相切.若点
在该球面上,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141ef400af3ec09829c4a640867acea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c510b85dfbca0e3ab0744655d77e8c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.存在点![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.若直线![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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