如图,
,点
在
上,过点
作
的平行线交
于点
,交过点
的直线于点
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/d0a15172-48e2-4e76-a639-de8782fc8011.png?resizew=129)
(1)求证:
是
的切线;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857928c314a347f3341e7ffbebd63e79.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/d0a15172-48e2-4e76-a639-de8782fc8011.png?resizew=129)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cf954378eca1e0383020c48bbf905c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
更新时间:2023-12-14 20:09:14
|
相似题推荐
解答题-问答题
|
适中
(0.65)
【推荐1】已知,如图 ,在
中,
于点D,以
为直角边作等腰直角△ACP,连接
交
于点E;
![](https://img.xkw.com/dksih/QBM/2023/10/13/3345205063819264/3361303501144064/STEM/e786b4e07239464b91986720851f3ce9.png?resizew=201)
(1)若
,则
的度数为_______°;
(2)求
的度数;
(3)若
,求
的值;
(4)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dd37bdc8ebd0561555e698ee7f1bc6.png)
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29434de3e5747921681bea1d6701e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2023/10/13/3345205063819264/3361303501144064/STEM/e786b4e07239464b91986720851f3ce9.png?resizew=201)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489cc69d529f52211985acbc20524de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ed5e3d39698f7c4d8369ed8a76a09c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f5a0ed106220423cfd0498f86be256.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e1c66eb7a4c7313af1266dbe2e8269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1a78c31e75d2eb6a3168de3d6edd41.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dd37bdc8ebd0561555e698ee7f1bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21670f6d2aa89395cc3ba2964a122625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3137705cb4170baafa66ff46eefb7a.png)
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【推荐2】如图,在
中,D是BC上一点,
,E、F分别是AC、BD的中点且
.已知
,
,求EF和AB的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ddd49625097d0a78df7170be4f882e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4a54cc7818be87a239f6de5f5d05b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df24f0ff17070e9a6592baea444b418.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/17/12f8e970-a133-4a3d-bdf2-96eeffe4edbb.png?resizew=176)
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解答题-作图题
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名校
【推荐3】在学习实数时,我们知道了正方形对角线的长度是边长的
倍,所以等腰直角三角形的底边长是腰长的
倍.例如,图1中的四边形ABCD是正方形,
ABC是等腰直角三角形,则AC=
AB.
小玲遇到这样一个问题:如图2,在等腰三角形ABC中,AB=AC,∠BAC=45°,BC=2
,AD⊥BC于点D,求AD的长.
小玲发现:如图3,分别以AB,AC为对称轴,分别作出
ABD,
ACD的轴对称图形,点D的对称点分别为E,F,延长EB,FC交于点G,可以得到正方形AEGF,根据轴对称图形的性质和正方形四条边都相等就能求出AD的长,请直接写出:BD的长为 ,BG的长为 ,AD的长为 ;
参考小玲思考问题的方法,解决问题:
如图4,在平面直角坐标系xOy中,点A(3,0),B(0,4),AB=5,点P是
OAB外角的角平分线AP和BP的交点,直接写出点P的坐标为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
小玲遇到这样一个问题:如图2,在等腰三角形ABC中,AB=AC,∠BAC=45°,BC=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
小玲发现:如图3,分别以AB,AC为对称轴,分别作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
参考小玲思考问题的方法,解决问题:
如图4,在平面直角坐标系xOy中,点A(3,0),B(0,4),AB=5,点P是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/2021/11/9/2847369672392704/2847788620644352/STEM/9d0f5ac4-91b0-438c-ae58-135b9c39b69c.png?resizew=614)
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【推荐1】在平面直角坐标系中,点
,点
,将
绕点B顺时针旋转,得
,点A,O旋转后的对应点为
,
,记旋转角为
.
时,点
的坐标为______,点
的坐标为______;
(2)如图②,当
时,求点
的坐标;
(3)连接
,设线段
的中点为M,连接
,求线段
的长的最小值(直接写出结果即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d1e4a02f6a99a4b838dcaf9541d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd9e1ebf9609e41bb0309a61650dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabe8be93ab57287ca5751ca98fce8ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c69a23d106fd34aa17b22e9c9a8de36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
(2)如图②,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fce10478485ef01d2318fc3465bb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fce10478485ef01d2318fc3465bb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6072f215a1d76152831efea49910d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6072f215a1d76152831efea49910d2a.png)
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【推荐2】如图,在Rt△ABC中,∠ACB=90°,D是斜边AB的中点,把△BCD沿BC翻折得到△BCE,作EF⊥AB于点F.
![](https://img.xkw.com/dksih/QBM/2021/9/16/2809119082487808/2810970971979776/STEM/d371b380ec194078b4cff420150ddaa3.png?resizew=174)
(1)求证:四边形BDCE是菱形;
(2)若AC=12,AB=20,求EF的长.
![](https://img.xkw.com/dksih/QBM/2021/9/16/2809119082487808/2810970971979776/STEM/d371b380ec194078b4cff420150ddaa3.png?resizew=174)
(1)求证:四边形BDCE是菱形;
(2)若AC=12,AB=20,求EF的长.
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【推荐1】如图,点E是
的内心,AE的延长线交BC于点F,交
的外接圆
点D.过D作直线
.
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899480794136576/2900181602131968/STEM/23abc046-a0a4-449c-aaa2-e9d75e754817.png?resizew=185)
(1)求证:DM是
的切线;
(2)求证:
;
(3)若
,
,求
的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](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/59523e10ca226529a8847492bf6a41c6.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899480794136576/2900181602131968/STEM/23abc046-a0a4-449c-aaa2-e9d75e754817.png?resizew=185)
(1)求证:DM是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f94cb32b388456ab9203e8d8b5309e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fc64a6b3e71b23a5ccb371967edfd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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解答题-证明题
|
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【推荐2】如图
所示,已知
,
是
的直径,
是
延长线的一点,
的弦
交
于点
,且
,
.
(1)如图
,求证:
是
的切线;
(2)在图
,连接
,
,若
,求
的值;
(3)如图
,连接
交
于点
,过
作
于点
,若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3767efa8adfb71001ad39df9560cbf6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b68e355a4e805a68e8c7fd4cf07cbd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/16/ad10bbc7-7de2-42fb-b8a6-4d24ec7f69ad.png?resizew=352)
(1)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)在图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04dab53e8b038f0b696e966acda03cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cae38316b0a61f630ff1b4e68a1cfa1.png)
(3)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9a087577b54c3941f701cc01813e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3d7ee77dd14bfd2e91d169c7009f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83006ff0795c44dd4f553aba38a425d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
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