名校
1 . 如图,在菱形
中,
,
,
、
分别为
、
上的点,
,
,若线段
上存在一点
,使得
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1fca278ad073e7a67642ababf077.png)
____ ;若
,则
的最大值为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acd69f9a7b4f4b7176eba8a2388631c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c0f3e6987b64c46a9fddbf1588510b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb064f478d74e6a2af2553206f875b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1fca278ad073e7a67642ababf077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05684d6873a8805e13bd454d8070389a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c6eb9d2c645f5eb5bed799b3b8137.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/75b82c47-05c7-4cd3-b437-cf6635da3513.png?resizew=202)
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945次组卷
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4卷引用:天津市耀华中学2022届高三下学期高考前冲刺(三)数学试题
名校
2 . 如图是由两个有一个公共边的正六边形构成的平面图形
,其中正六边形边长为1.设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
________ ;
是平面图形
边上的动点,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5debfa10a860aa531003db3de20d0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62781e998c5d72e938d57ed2cf555a10.png)
![](https://img.xkw.com/dksih/QBM/2022/3/18/2938998989365248/2941860681621504/STEM/10cf25fdff6b45099241b30ebd6c331b.png?resizew=178)
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2022-03-22更新
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1939次组卷
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8卷引用:天津市第一中学2022届高三下学期统练6数学试题
名校
3 . 如图,在
中,
,
,
,
分别为
,
的中点,
为
与
的交点,且
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
___________ ;若
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979fe4251a15b870fc6416b2fcd86676.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92f0c583cc9daf980a8621ad96aef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70cc587dbef0d91446ee5f36384eaffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be83c43186f9919e2c7eb2aefa1d3d51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979fe4251a15b870fc6416b2fcd86676.png)
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2022-03-10更新
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3654次组卷
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16卷引用:天津市耀华中学2022届高三下学期统练11数学试题
天津市耀华中学2022届高三下学期统练11数学试题天津市耀华中学2023届高三下学期大统练5数学试题天津市区重点中学2022届高三下学期一模联考数学试题天津市滨海新区塘沽第一中学2022届高三下学期4月线上统练数学试题天津市区重点学校2022届高三下学期二模数学试题(已下线)2022年高考押题预测卷01(浙江卷)-数学天津市滨海新区塘沽第一中学2023届高三上学期线上统练摸底考试数学试题云南省昆明市第十二中学2023届高三(普通班)下学期2月月考数学试题云南省宣威市第六中学2023届高三下学期2月月考数学试题天津市南开大学附属中学2023届高三下学期3月统练(二)数学试题天津市蓟州区第一中学2023-2024学年高三上学期第二次学情调研数学试题(已下线)信息必刷卷02(天津专用)江苏省无锡市天一中学2021-2022学年高一下学期期中数学试题江苏省苏州市昆山中学2021-2022学年高一下学期期末数学试题(已下线)期末考试仿真模拟试卷04-(苏教版2019必修第二册)天津市武清区杨村第一中学2023-2024学年高一下学期第三次月考数学试卷
4 . 在△
中,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422a1fef34cc5b27fe3c9ec1aa95546d.png)
___________ .点
在直线
上运动,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d11a5a756d8fdd7b294c4f5fd63467b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc42598fc484288db571f85b96898c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422a1fef34cc5b27fe3c9ec1aa95546d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37b6118f80d874d2c857fc9632977d0.png)
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3卷引用:天津市第一中学2022-2023学年高三下学期4月月考数学试题
名校
解题方法
5 . 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”,亦称为“赵爽弦图”(1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).类比,可构造如图所示的图形,它是由三个全等的三角形与中间一个小等边三角形组成的一个较大的等边三角形,设
且
,则可推出![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592c6fdbe79a05318d5b1ef7610ecada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e5b4ac18aa3fb858c72ee906345a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
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2021-12-04更新
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2236次组卷
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8卷引用:天津市耀华中学2021-2022学年高三上学期第二次月考数学试题
天津市耀华中学2021-2022学年高三上学期第二次月考数学试题天津市耀华嘉诚国际中学2021-2022学年高一下学期期中数学试题(已下线)专题2 赵爽弦图(已下线)专题2平面向量的坐标运算 (提升版)(已下线)FHgkyldyjsx08(已下线)第05讲 平面向量基本定理-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第二册)福建省厦门双十中学2021-2022学年高一下学期第一次月考数学试题浙江省北斗联盟2023-2024学年高一下学期4月期中联考数学试题
解题方法
6 . 已知直角梯形
中,
,E是线段
上靠近A的三等分点,F是线段
的中点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411cb28bfde7b1ec9e53165f666e5f3b.png)
________ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f63d194aa0d4091618b6f41f569ee2.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5372776176f715480c7641ab6686610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411cb28bfde7b1ec9e53165f666e5f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd6407c804c5ad9a0faf6532482a6d48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f63d194aa0d4091618b6f41f569ee2.png)
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2021-06-08更新
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684次组卷
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4卷引用:天津市益中学校2022-2023学年高三上学期第一次学情调研数学试题
天津市益中学校2022-2023学年高三上学期第一次学情调研数学试题天津市南大奥宇学校2021届高三下学期高考模拟数学试题(已下线)考点19 平面向量的数量积及向量的应用-备战2022年高考数学(文)一轮复习考点帮天津市宝坻区大口屯高级中学2021-2022学年高三上学期第一次月考数学试题
名校
7 . 在平行四边形
中,
,
相交于点
,
为线段
上的动点,若
,则
的最小值为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b957b0edd813f0a04ec5dcaaf1817e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c06c3dd8b12d1cdfd5fb66b0d6568d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef47626be84de5fe7a54a5a5db5082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdaa39214f9b923d7510b3cafbbe279.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/c9cfc028-8041-48e2-afa9-7b9c8e94af13.png?resizew=216)
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2021-05-21更新
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2684次组卷
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11卷引用:天津市第一中学2021-2022学年高三上学期第三次月考数学试题
天津市第一中学2021-2022学年高三上学期第三次月考数学试题天津市宝坻区2021届高三下学期高考模拟练习一数学试题天津市滨海新区塘沽第一中学2020-2021学年高三上学期第二次月考数学试题(已下线)2021年新高考天津数学高考真题变式题11-15题天津市静海区第一中学2021-2022学年高三上学期12月学生学业能力调研数学试题天津市第四十七中学2022届高三下学期学业能力调研数学试题(已下线)技巧02 填空题的答题技巧(精讲精练)-2(已下线)技巧02 填空题的答题技巧(8大题型)(练习)上海市金山中学2020-2021学年高一下学期期末数学试题上海市华东师范大学第三附属中学2021-2022学年高一下学期期末数学试题上海市复旦大学附属中学青浦分校2022-2023学年高一下学期3月月考数学试题
名校
8 . 平行四边形
中,
,
为
上的动点,
,
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f855c80172c04310d342f82d960011ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd77df02ee5da142f4161d737f4ba05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b64af28c24767dd9a64e49e5948c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3af6f75cee73a485c49e63a8b642f7.png)
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名校
9 . 已知平行四边形
的两条对角线相交于点
,
,
,
,其中点
在线段
上且满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185061adb1814245b4b513739c55d37b.png)
______ ,若点
是线段
上的动点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b19819443514c14e3133a657941198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e62790b80d4dd6e19ef709088eec57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3459f40bcad3f91600a8ab0f9a3b1a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185061adb1814245b4b513739c55d37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ce4aa176b1dc89d49a7b05806b35ef.png)
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7卷引用:天津市第二南开学校2021-2022学年高三上学期期中数学试题
名校
10 . 如图,在
中,
,
,D,E分别是直线
,
上的点,
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4397f6e86c69e6b597e7e8635afbfb8.png)
_____ .若P是线段
上的一个动点,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d386c4cd13d9fe9af2382960b71489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5762ef8627372fd72cd44cade28da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bba98b56e956fca9aaab0c7c817300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4397f6e86c69e6b597e7e8635afbfb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e24b08c76424e808009e2dc811193af.png)
![](https://img.xkw.com/dksih/QBM/2021/1/18/2638645483511808/2639335091822592/STEM/cce4295a-08c8-43b1-b12d-ed79ca7ff2aa.png?resizew=213)
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936次组卷
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4卷引用:天津市第一中学2020-2021学年高三上学期第三次月考数学试题
天津市第一中学2020-2021学年高三上学期第三次月考数学试题天津市天津中学2022-2023学年高三上学期期末线上自测数学试题(已下线)模型1 平面向量几何意义的应用模型(高中数学模型大归纳)苏教版(2019) 必修第二册 过关斩将 章节测试 第9章 平面向量