阅读下列材料,完成相应的任务.
婆罗摩笈多(Brahmagup1a)是古印度著名数学家、天文学家,他在三角形、四边形、零和负数的算术运算规则、二次方程等方面均有建树,特别是在研究一阶和二阶不定方程方面作出了巨大贡献.他曾经提出了“婆罗摩笈多定理”,该定理也称为“布拉美古塔定理”,该定理的内容及部分证明过程如下:
布拉美古塔定理:已知:如图1,四边形
内接于
,对角线
,垂足为
,点
为
的中点,连结
并延长,交
于点
,则
.
证明:
,
,
,
(依据),
,
…
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/59e02512-90ad-455e-acbd-22abd339f342.png?resizew=347)
(1)上述证明过程中的依据是指______.
(2)请补全上述证明过程.
(3)请利用布拉美古塔定理完成如下问题:如图2,三角形
内接于
,
,点
是弧
的中点,
,请直接写出线段
的长度.
婆罗摩笈多(Brahmagup1a)是古印度著名数学家、天文学家,他在三角形、四边形、零和负数的算术运算规则、二次方程等方面均有建树,特别是在研究一阶和二阶不定方程方面作出了巨大贡献.他曾经提出了“婆罗摩笈多定理”,该定理也称为“布拉美古塔定理”,该定理的内容及部分证明过程如下:
布拉美古塔定理:已知:如图1,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0e7a1541a8db0c059fd6cd0c4c3620.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8e5b894eabf591a4dbaaea258b438a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c8f0f573021b130dd15677f3ed96d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5c950b6696c2dc39868594482d455c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bf66323347a8b28c8b123b0ab25e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a220a5e2c39af6f6490686cc7875d17.png)
…
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/59e02512-90ad-455e-acbd-22abd339f342.png?resizew=347)
(1)上述证明过程中的依据是指______.
(2)请补全上述证明过程.
(3)请利用布拉美古塔定理完成如下问题:如图2,三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0aa16fb65d38e6d95f02c8d34a85b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
更新时间:2024-02-28 15:16:44
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】如图,点D为等腰直角三角形
斜边
上一动点(点D不与线段
两端点重合),将
绕点B顺时针方向旋转
到
,连接
.
(1)求证:
;
(2)若
,求
的长:
(3)若
,请直接写出
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d2efd1372825a8f5d5f9c4f3aa1c99.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/33c2788e-748f-47db-9219-7b657ac03dc7.png?resizew=116)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2292702ebc75724359ed36184438db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e8f51c6e746877851128a5a21c0446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d9cc878828cb1b2c85d04ca025c570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c9b93e22e22cb7b5999929c5fc13df.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在△ABC中,BD⊥AC于D,DC=2AD.以DC为直径作半圆O,交BC于点E,且BD=2BE=2.连接OB,过点D作DF⊥OB交
于点F,垂足为G,连接BF.
(1)求⊙O的半径R;
(2)求证:∠DBF=2∠ABD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8192018a58bb1fe23769a48a4d9042ed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/c1bf2eae-32b7-484b-8d2c-d6581b76a18d.png?resizew=190)
(1)求⊙O的半径R;
(2)求证:∠DBF=2∠ABD.
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】如图,在正方形
中,射线
与边
交于点E,将射线
绕点A顺时针旋转,与
的延长线交于点F,
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/6bf8307d-e107-476d-a616-0743cc7d97aa.png?resizew=176)
(1)求证:
是等腰直角三角形;
(2)若四边形
的面积为36,
,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03687d97d61b4a7cecbb73f2a6604212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c57b07f75e97d9f84718bd495ebcf4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/6bf8307d-e107-476d-a616-0743cc7d97aa.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910936ec9fb419d51ce2f5ea817f8401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,点
是正方形
内一点;点
到点A,B和
的距离分别为
和
.
是等腰直角三角形,连接
,延长
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/4d417b3e-dc3e-4d1e-9af0-eb8c0a540f98.png?resizew=129)
(1)求证:
.
(2)求
的大小.
(3)求正方形
的边长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76494515d56bf4efc218ac621bb1fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2f90f1f950f19b10ee0b1852cec730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c733c8bb6ee8666dc5477d5fb8c6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/4d417b3e-dc3e-4d1e-9af0-eb8c0a540f98.png?resizew=129)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6c589c8a6845f280d8098e2c1c6121.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb967f3188ad239a78047edf98458d6.png)
(3)求正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
【推荐1】如图,
是
的内接三角形,
是
的直径,
,利用尺规作图法,在弧
上求作点
使得.
(保留作图痕迹,不写作法).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52459d2cf85be6684f93828daeb7a32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2e935fc648ea56b8d66b60cdae0140.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,
是
的直径,
是弦,且
于点E,
交
于点F,连接
、
,若
.
是
的切线;
(2)若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11c1db76cc7e1894f74a50d71736455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1789641e8179f87a5afb058999bbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
【推荐1】如图,梯形
中,
,对角线
,
,点E是边
上一点,
,
,
交
于点F、交
延长线于点G,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbd4748f0b3b3f10bf8d9421d1806b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d2231c7a2875ab6d423dff3ead4069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7eb44b7bb29b11e975805ecdacad521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/ab849159-9664-4dbe-b1dd-d680b447531a.png?resizew=202)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】如图所示,在
中,
,
,点
从
点出发,沿着
以每秒
的速度向
点运动;同时点
从
点出发,沿
以每秒
的速度向
点运动,设运动时间为
.
![](https://img.xkw.com/dksih/QBM/2019/12/6/2349307617599488/2350190539481088/STEM/264dc0409d96420a8cad7b90bd8106b5.png?resizew=186)
(1)当
为何值时,
;
(2)当
,求
的值;
(3)
能否与
相似?若能,求出
的长;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b10a49d4f2473d9448968fe9e32b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e79c6ea999ff37689003bae31c81dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244ea6a312d4b6831a6b833ea3f4fcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f319d8ffd15a6ce36ca7aecad4fd087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2019/12/6/2349307617599488/2350190539481088/STEM/264dc0409d96420a8cad7b90bd8106b5.png?resizew=186)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa884503e7d2137a11f67d74bb79f0c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d330f370a54165fbcb3fb11df5debe5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7a2295c716cd6ec8b7ee61d4a5e773.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc3919b5000f9af77ddb77a62bee9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef9bdc192e9dbd249cc4e66f144b469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
您最近一年使用:0次