解题方法
1 . 记
的内角A、B、C的对边分别为a、b、c,已知
.
(1)证明:
;
(2)若角B的平分线交AC于点D,且
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70298774083c0ed8fab9cbf5ba6a034c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d8ba5d74557ac0660343e61b3bd8f.png)
(2)若角B的平分线交AC于点D,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16843ba124e1569767450fa674b1326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f8579ee0af5c0bf270354e30e11584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
2 . 从①
;②
;③
,这三个条件中任选一个,补充在下面的横线上并解答问题.
在锐角
中,角
所对的边分别为
,且________.
(1)证明:
;
(2)求
的取值范围.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61520d282e01646a83520adb34bb268f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe783f8edcd57d3d006402f20e299ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66313f925fab8738610ebec46b011b2e.png)
在锐角
![](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/76f0649064a085fb74c997fb507a9b6d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8904522bf844b61febddc24346f8232f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d08d3424de01407954a0a8649374eaf.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2023-10-07更新
|
443次组卷
|
3卷引用:河南省部分学校2023-2024学年高三上学期一轮复习摸底测试卷数学(三)
河南省部分学校2023-2024学年高三上学期一轮复习摸底测试卷数学(三)四川省叙永第一中学校2024届高三上学期数学(理)“一诊”模拟测试(二)试题(已下线)专题12 正余弦定理妙解三角形问题和最值问题(练习)
解题方法
3 . 记
的内角A,B,C的对边分别为a,b,c,且
.
(1)求证:
,
,
是等差数列;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d28942c052d6686821ec146d5c3fb0b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e5d4f93699f8dcffb0e7840ca5597e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b01adc561735ff5be9bb97266918f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32e2f2d7147cf1699fbfdef9cf4af74.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a24a8f5e8fb89381f8add6549170345.png)
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解题方法
4 . 已知
的外心为
,点
分别在线段
上,且
恰为
的中点.
(1)若
,求
面积的最大值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae77843b579fb22b88b1fc20ddddd0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ba0689fc06b00357c42e59424f21b4.png)
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5 . 在
中,角
,
,
所对的边分别为
,
,
,
.
(1)求证:
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/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/3c4497635b33adc89d4669439236abbe.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1871203419c14bbe078f220b302343.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97757fd876c0ea02758e3beceb64a5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32f2d4d1d2c16c54b2caef17840bfcb.png)
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解题方法
6 . 设
的内角
的对边分别为
,且
.
(1)证明:
;
(2)若
,且
的面积为3,求
的内切圆面积.
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa28638ff47ed04fe1d047adb5a260a3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dac5d93626207b69691c7f24de97009.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09921d9904335a83078262ce62a473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2023-08-04更新
|
952次组卷
|
3卷引用:福建省福州第四中学2023届高三考前适应性考试数学试题
解题方法
7 . 已知a,b,c分别为
三个内角A,B,C的对边,且
.
(1)证明:
;
(2)若
,
,
,求AM的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35314b7942eae29de8b67b578f7c4c8d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12afa49ce117afc97c5261a0364a9cc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819c7a62f0c3f64f53370d19db912c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecb91d19a693299dcdad4059b6237a1.png)
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2023-07-25更新
|
145次组卷
|
2卷引用:福建省福州市八县(市)协作校2022-2023学年高二下学期期末联考数学试题
名校
解题方法
8 . 记
的内角
的对边分别为
.
(1)证明:
;
(2)若
,求
.
![](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/0df9f69852dac5143b7bcfc72d376ce3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122a10469b30d702e0a5e8524717319b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988b7e964e313579ab8869d67d5be007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
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解题方法
9 . 在
中,设内角
,
,
所对的边分别为
,
,
.若
.
(1)证明:
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/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/72c573728c6d5c61cb02dea29b03db1c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43e603c47efbbcb8570bd9a4891b679.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fba806556be445adb6fa65774ed091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5201fc26d013f6fb889933c0e32f5c53.png)
您最近一年使用:0次
2023-07-08更新
|
235次组卷
|
2卷引用:广东省肇庆市2022-2023学年高一下学期期末数学试题
名校
解题方法
10 . 古希腊的数学家海伦在其著作《测地术》中给出了由三角形的三边长a,b,c计算三角形面积的公式:
,这个公式常称为海伦公式.其中,
.我国南宋著名数学家秦九韶在《数书九章》中给出了由三角形的三边长a,b,c计算三角形面积的公式:
,这个公式常称为“三斜求积”公式.
(1)利用以上信息,证明三角形的面积公式
;
(2)在
中,
,
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684c13a2cea962fb204256ca433a4d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a822dd4e1d3859f55874669092697a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bd5fefb9a7c618d1ef8d73b3c43cd4.png)
(1)利用以上信息,证明三角形的面积公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634fdb49ecc32befaf9ac4ce84ae5a37.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dcdf048e907e670072f1070c8a8b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3696bff45e67a5a0cbd0ca5b253e3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-07-06更新
|
1047次组卷
|
4卷引用:广东省广州市白云区2022-2023学年高一下学期期末数学试题
广东省广州市白云区2022-2023学年高一下学期期末数学试题浙江省2023-2024学年高一下学期3月四校联考数学试题河南省信阳市新县高级中学2024届高三4月适应性考试数学试题(已下线)专题02 第六章 解三角形及其应用-期末考点大串讲(人教A版2019必修第二册)