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解题方法
1 . 大约在公元222年,赵爽为《周髀算经》一书作序时介绍了“勾股圆方图”,亦称“赵爽弦图”(如图1).某数学兴趣小组类比“赵爽弦图”构造出图2:
为正三角形,
,
,
围成的
也为正三角形.若
为
的中点,①
与
的面积比为___________ ;②设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
___________ .
![](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/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e507d3941363e9dbeac8be35134727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/c1bd98f1-c926-4719-b25c-602039f53dd5.png?resizew=272)
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2023-05-05更新
|
1791次组卷
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4卷引用:安徽省六安第一中学2023届高考适应性考试数学试题
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2 . 若平面上不共线的四点
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c95c6fedd33a4a8b2d25c4a2bd8d077.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7147ca48d60f169fab98d1f8aa3287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a7f4ad019cbd40a95cd77c858743ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98499dbd54f2db27b8c4d97fdcaec4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c95c6fedd33a4a8b2d25c4a2bd8d077.png)
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3 . 已知双曲线
:
,圆
:
与x轴交于
两点,
是圆О与双曲线在x轴上方的两个交点,点
在y轴的同侧,且
交
于点C.若
,则双曲线的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd2419f7bffae4789adc7de33cbdd84.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/8c933b121496d87292fba89f1b24913b.png)
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2023-04-23更新
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4卷引用:安徽省安庆市田家炳中学2022-2023学年高二下学期第二届“校长杯”竞赛数学试题
安徽省安庆市田家炳中学2022-2023学年高二下学期第二届“校长杯”竞赛数学试题湖南省永州市2023届高三三模数学试题湖北省恩施市第二中学2023届高三适应性考试数学试题(已下线)第3讲:圆锥曲线的定义以及应用【练】
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4 . 如图所示是毕达哥拉斯的生长程序:正方形上连接着等腰直角三角形,等腰直角三角形边上再连接正方形,如此继续,设初始正方形ABCD的边长为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dd5b7be65e7b3d3e768abc4ccbfb61.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dd5b7be65e7b3d3e768abc4ccbfb61.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/48506040-0768-407a-8e0e-1e8b7ea3900c.jpg?resizew=245)
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5 . 如图,设
为
内一点,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2f8dfc73832b3cd45f5cfecc250444.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/7fdf361413829342270719bababf91c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2f8dfc73832b3cd45f5cfecc250444.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/2ecb0a81-1ab9-4659-a494-95910170859e.png?resizew=130)
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2023-03-05更新
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1437次组卷
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4卷引用:安徽省合肥市第一中学2022-2023学年高一下学期第一次月考数学试题
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6 . 在△ABC中,点D满足
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd989ddfbed4a6aa18ea57734522153.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66165a4813c742ee07a2b4a96887c458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f246e768453547ea87c73dd527e2a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd989ddfbed4a6aa18ea57734522153.png)
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2023-02-22更新
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2卷引用:安徽省淮北市树人高级中学2023-2024学年高二上学期开学检测数学试题
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7 . 如图,在
中,
,点P为边BC上的一动点,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b61b04e79b1549a2e98403fb99a627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3af6f75cee73a485c49e63a8b642f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/1745b797-f9d1-4e31-ac44-fdd07c314f21.png?resizew=186)
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2022-07-08更新
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