【揭示关系】如图1,在
中,
,
,
,则
,
.即
.因此,对于含
角的直角三角形的三边关系,可以作为问题解决的条件直接使用.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/04fe017b-9c24-477d-bad1-e42b58ea2605.png?resizew=541)
【问题解决】
(1)如图2,在
中,
,
,点C在边
上,点D在
边上,
,点E,F分别为
、
的中点.则
,
.
(2)将
绕点O逆时针旋转
后,得到
,点C,D的对应点分别为点
,
,连接
,
,得到图3.若点M是
的中点,连接
.
①求证:
;
②线段
和
之间存在怎样的数量关系和位置关系?写出你的结论,并进行证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69eef1ee07929ee09efe0155a14f1524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/04fe017b-9c24-477d-bad1-e42b58ea2605.png?resizew=541)
【问题解决】
(1)如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c633830c6e2ac6d8d6e18890ef5ee33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1df17440481c8da8e0a17f008dbc4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bee54b66cb4534176395678c8a89eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d1dca8fdfc5017ccb2a549d822281a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43f43bc8b26d8705f0cbaafa291ad96.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a1ac98b67f419d0dd69f4b8126a77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147f7bacdbf960a2e0809bafc3bc1527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b34402b3d73ea9ecd81934fc9bf358f.png)
②线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
更新时间:2023-01-07 12:15:15
|
相似题推荐
解答题-作图题
|
较难
(0.4)
名校
【推荐1】【教材呈现】下图是华师版九年级上册数学教材第77页的部分内容.
【定理证明】(1)请根据相似三角形的判定定理的相关内容,结合图①,写出证明过程.
【定理应用】:
(2)如图②,在
中,
垂直于
的平分线
于点E,且交
边于点D,点F为
的中点.若
,
,则
的长为_____________.
(3)如图③,在矩形
中,
,
,点E在边
上,且
.将线段
绕点A旋转一定的角度
,得到线段
,连结
.点H为
的中点,连结
.设
的长度为m.则m的最大值为_____________.
猜想:如图.在![]() ![]() ![]() ![]() ![]() ![]() |
【定理应用】:
(2)如图②,在
![](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/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.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/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)如图③,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2e57629856cc8ed7ab28ca9ca76d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1661f96d88125ebd75eee28806841bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf97f9082d7f40bc680cc2c58865309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f0ae0d8e74c9ca1708ce83c36c94df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f0ae0d8e74c9ca1708ce83c36c94df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/9d5a6336-9954-4fad-ae7a-9b550f8be6fb.png?resizew=550)
您最近一年使用:0次
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【推荐2】如图1,一根木棒AB,斜靠在与地面OM垂直的墙壁ON上,当木棒A端沿NO向下滑动时,同时B端沿射线OM向右滑动,实践发现木棒的中点P运动的路径是一个优美的几何图形,我们把这样的点叫优美点.如果木棒AB长为4,与地面的倾斜角∠ABO=60°.
(1)当木棒A端沿NO向下滑动到点O时,同时B端沿射线OM向右滑动到B′时,木棒的中点P所经过的路径长为多少?
(2)若点P为OB上由点O向点B运动的一运动点,连接AP.
①如图2,设AP的中点为G,问点G是不是优美点,如是,请求出点P运动过程中G所经过的路径长.
②如图3,过点B作BR⊥AP,垂足为点R.点P运动过程中,点R是不是优美点,如是,请求出点R所经过的路径长.
(3)如图4,若点P以每秒1个单位长度由点B向点O运动,同时点Q以每秒
个单位长度的速度由点A向点O运动,连接PQ,S为PQ的中点,则在PQ的运动过程中,点S经过的路径长为多少?(直接写结果)
(1)当木棒A端沿NO向下滑动到点O时,同时B端沿射线OM向右滑动到B′时,木棒的中点P所经过的路径长为多少?
(2)若点P为OB上由点O向点B运动的一运动点,连接AP.
①如图2,设AP的中点为G,问点G是不是优美点,如是,请求出点P运动过程中G所经过的路径长.
②如图3,过点B作BR⊥AP,垂足为点R.点P运动过程中,点R是不是优美点,如是,请求出点R所经过的路径长.
(3)如图4,若点P以每秒1个单位长度由点B向点O运动,同时点Q以每秒
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/3/fc1fec68-d69d-452c-857b-8e1b45ec3ec1.png?resizew=498)
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【推荐3】在中点复习课中,刘老师提出了如下问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/34f59f50-8471-403e-a5c4-4bc3a8fecaad.png?resizew=359)
如图1,在
中,点D为
的中点,连接
,若
,求
的取值范围.
【初步分析】
小明经过分析,决定延长
到E,使
,连接
,可得到
,进而在
中得到
的取值范围,于是可求得
的取值范围.
(1)请回答:
①如图1,连接
,由已知和作图能得到
的理由是______.
A.
B.
C.
D.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5eb2decaa6be2df36a5e4b7fabf585d.png)
②求得
的取值范围是______.
A.
B.
C.
D.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a6731ca8823b4b3d78367a1cb86f52.png)
【感悟探究】
小明经过反思发现,解题时,条件中若出现“中点”“中线”字样,可以考虑延长中线构造全等三角形,把分散的已知条件和所求证的结论集合到同一个三角形中.
于是小明尝试用这种方法证明“中位线定理”
如图2,
分别是
的边
的中点,求证:
,且
.
小明延长
至F,使
,连接
.
(2)请帮助小明完成证明.
【感悟拓展】
小明经过再次反思发现,解题时,条件中若出现多个“中点”字样,还可以考虑用中位线来研究中位线和三角形底边的数量关系和位置关系.请解决以下问题:
(3)如图3,在等边三角形
中,点P为射线
位于点C右侧的一个动点,将线段
绕点P逆时针旋转
得到线段
,点C的对应点为点D,连接
,点Q为
的中点,连接
.若
,当
时,直接写出
的长度.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/34f59f50-8471-403e-a5c4-4bc3a8fecaad.png?resizew=359)
如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f83dded14ac36a1b267a52e0e8522d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
【初步分析】
小明经过分析,决定延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df34369163e511f14028168cb0b21186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7d19b5c22d55256a532764d4a8a5b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80651f797ab9dccfd7163c605b091ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(1)请回答:
①如图1,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30344bc4e9906892f903e1f0b691c18.png)
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6720e36b02193db161c61d4017673760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a290f047f50481318d040c604d72f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9beb8b968744573e593ac28451c69729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5eb2decaa6be2df36a5e4b7fabf585d.png)
②求得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb89f323547493204e1550f32e94e9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b04633aebfef3b31813acf2f221355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288d232ff62a35acdf9bf8e706b95aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a6731ca8823b4b3d78367a1cb86f52.png)
【感悟探究】
小明经过反思发现,解题时,条件中若出现“中点”“中线”字样,可以考虑延长中线构造全等三角形,把分散的已知条件和所求证的结论集合到同一个三角形中.
于是小明尝试用这种方法证明“中位线定理”
如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066cd386723885c535ea720f5817847a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0584568387d42bb65fff6fe354f1117a.png)
小明延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9a9618018d717926540d1452f76e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)请帮助小明完成证明.
【感悟拓展】
小明经过再次反思发现,解题时,条件中若出现多个“中点”字样,还可以考虑用中位线来研究中位线和三角形底边的数量关系和位置关系.请解决以下问题:
(3)如图3,在等边三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809f2107a6172278be8675645f1c186d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
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解答题-证明题
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【推荐1】如图1,在四边形
中,
是等边三角形,点
是直线
上(异于点
)的动点,点
绕着点
逆时针旋转
至点
处,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/689032ca-221d-40c3-9671-3d4d85764e56.png?resizew=394)
(1)
______
.
(2)当点
在线段
上时,如图2,连接
.
①求证:
;
②在线段
上一定存在一个定点
,满足
,请说明理由.
(3)当点
在直线
上时,②中的结论还成立吗?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd2cbeb3aa0f401e46782b10122247b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/689032ca-221d-40c3-9671-3d4d85764e56.png?resizew=394)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b63f7bb04b2ddc7c88d0363a812a22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce1475f537b4ad21775bfaa16daa0c.png)
②在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77240fccf57533b2d56d2591b094b94.png)
(3)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐2】实验与操作:
在
中,
,将
绕点
按顺时针方向旋转得到
(点
分别是点B,C的对应点),设旋转角为
,旋转过程中直线
和线段
相交于点
.
猜想与证明:
经过点
时,探究下列问题:
I.此时,旋转角
的度数为____________.
II.连接
,判断此时四边形
的形状,并证明你的猜想.
(2)如图②所示,当旋转角
时,求证:
.
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce7f6d278f2ef7a193b7eed7be6b3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6326727a37e3fe8c1833bc41c2ee65db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce7f6d278f2ef7a193b7eed7be6b3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dfcdd5f7f80c628800f3884510a38e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c8da9efcd45a4ac55eb1ca203b77d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1110033382e192b1bc24e9682a2e73c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c431cd12f858f0bc8dabb1d8c0b8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
猜想与证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
I.此时,旋转角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
II.连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0866400a6b27152080c81d81f0cfbea1.png)
(2)如图②所示,当旋转角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec8fc3496c7499cc59f4b4ace8a2999.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐1】在平面直角坐标系中,已知抛物线
经过
两点.P是抛物线上一点,且在直线
的上方.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/98364d40-212b-4ad6-a42a-e4e6d77207ba.png?resizew=189)
(1)求抛物线的表达式;
(2)若
面积是
面积的
倍,求点
的坐标;
(3)如图,
交
于点
,
交
于点D.记
,
的面积分别为
,判断
是否存在最大值.若存在,求出最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53be61cd85ec86aabd164cae0265246b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bba103baef3bf9eb6b3655d3ef601a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/98364d40-212b-4ad6-a42a-e4e6d77207ba.png?resizew=189)
(1)求抛物线的表达式;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e83c25d098876cfc55d2cbf39858367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31039dbbbcad3eaa3c85a3ddfeca2b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff36ac07c45c8d03cf3b7d8739c517ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b982b4ed3b75609bda6af3914986d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
【推荐2】如图,六边形
内接于半径为
(常数)的
,其中
为直径,且
.
![](https://img.xkw.com/dksih/QBM/2020/1/7/2371797983821824/2371899786371072/STEM/c0343a0cccd941749b2191709f85cb27.png?resizew=180)
(1)当
时,求
的长;
(2)求证:
;
(3)设
,求六边形
的周长
关于
的函数关系式,并指出
为何值时,
取得最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabafaf7dcd82ad5034318c0f22aadec.png)
![](https://img.xkw.com/dksih/QBM/2020/1/7/2371797983821824/2371899786371072/STEM/c0343a0cccd941749b2191709f85cb27.png?resizew=180)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edd00fc6f858bc44cb83543e3bbe70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c2c8f2401241cb53e5f56c3f2125c9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a3d679b4dae63575903387a76ce45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次