已知:如图,
是
的直径,
,
交
于点D,点E是
的中点,
与
的延长线交于点F.
![](https://img.xkw.com/dksih/QBM/2023/4/25/3224356101152768/3224699569258496/STEM/449b422aa0bc476e85452a1690ae7ca6.png?resizew=155)
(1)求证:
是
的切线;
(2)若
,
,求
外接圆的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee730f6a2551fb1b582ecf290cfea233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8946331b0a9d86e1a9c78797f3021455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/2023/4/25/3224356101152768/3224699569258496/STEM/449b422aa0bc476e85452a1690ae7ca6.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ccea461315a9d05aa0193b937d4bfe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f0dfb4b34d4fca6a18cea7c44a250e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8933996605e3a162782e6bfb34db9bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
2023九年级下·浙江·专题练习 查看更多[1]
(已下线)(挑战压轴)专项2.1 切线的证明方法归类(2大类型+5种方法)-2022-2023学年九年级数学下册《同步考点解读·专题训练》(浙教版)
更新时间:2023-04-26 10:10:58
|
相似题推荐
解答题-问答题
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解题方法
【推荐1】我们规定:线段外一点和这条线段两个端点连线所构成的角叫做这个点对这条线段的视角.如图1,对于线段AB及线段AB外一点C,我们称∠ACB为点C对线段AB的视角.
![](https://img.xkw.com/dksih/QBM/2015/2/10/1573798167691264/1573798173343744/STEM/a7f7121818b4426e8321317b13a34f52.png)
如图2,在平面直角坐标系
中,已知点D(0,4),E(0,1).
(1)⊙P为过D,E两点的圆, F为⊙P上异于点D,E的一点.
①如果DE为⊙P的直径,那么点F对线段DE的视角∠DFE为_________度;
②如果⊙P的半径为
,那么点F对线段DE的视角∠DFE为_________度;
(2)点G为x轴正半轴上的一个动点,当点G对线段DE的视角∠DGE最大时,求点G的坐标.
![](https://img.xkw.com/dksih/QBM/2015/2/10/1573798167691264/1573798173343744/STEM/a7f7121818b4426e8321317b13a34f52.png)
如图2,在平面直角坐标系
![](https://img.xkw.com/dksih/QBM/2015/2/10/1573798167691264/1573798173343744/STEM/cc1c248e23114c15a85122e394ac06ec.png)
(1)⊙P为过D,E两点的圆, F为⊙P上异于点D,E的一点.
①如果DE为⊙P的直径,那么点F对线段DE的视角∠DFE为_________度;
②如果⊙P的半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(2)点G为x轴正半轴上的一个动点,当点G对线段DE的视角∠DGE最大时,求点G的坐标.
![](https://img.xkw.com/dksih/QBM/2015/2/10/1573798167691264/1573798173343744/STEM/75bebdfa380946949e157543909bd699.png)
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解答题-作图题
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【推荐2】如图,
中,
,
.
(1)动手操作:利用尺规作以
为直径的
,并标出
与
的交点D,与
的交点E(保留作图痕迹,不写作法);
(2)综合应用:在你所作的图中,
①求证:
;②求点D到
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d363f7aac42c7adf8d2ddf05978d3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec569211c8d47b19c945e395e7395d99.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/2/5ab593a7-6d1c-41ba-a61e-69dc3806771d.png?resizew=146)
(1)动手操作:利用尺规作以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)综合应用:在你所作的图中,
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb485a5d4bbfcfd0d0e5d92a1882e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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解答题-作图题
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名校
【推荐1】如图,已知线段AB.
(1)仅用没有刻度的直尺和圆规作一个以AB为腰、底角等于30°的等腰△ABC.(保留作图痕迹,不要求写作法)
(2)在(1)的前提下,若AB=2cm,则等腰△ABC的外接圆的半径为 cm.
(1)仅用没有刻度的直尺和圆规作一个以AB为腰、底角等于30°的等腰△ABC.(保留作图痕迹,不要求写作法)
(2)在(1)的前提下,若AB=2cm,则等腰△ABC的外接圆的半径为 cm.
![](https://img.xkw.com/dksih/QBM/2018/5/4/1938008318386176/1940883942539264/STEM/3d51746af0184871a2120055499ad43e.png?resizew=123)
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解答题-作图题
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【推荐2】如图,在平面直角坐标系
中,
的三个顶点坐标分别为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/f903d001-34ba-45b0-ac84-7a54a3a1ae35.png?resizew=215)
(1)按下列要求画图;
①将
沿
轴向左平移
个单位长度,得到
,请画出
;
②将
绕点
逆时针旋转
,得到
,请画出
.
(2)
是 三角形,其外接圆的半径
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ed78ce963b0e7937e036a2393143cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/f903d001-34ba-45b0-ac84-7a54a3a1ae35.png?resizew=215)
(1)按下列要求画图;
①将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c3135fa20c32d04a270750f77c1f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c3135fa20c32d04a270750f77c1f2d.png)
②将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c3135fa20c32d04a270750f77c1f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152236216f8d1cb39b261108e8fc8b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403590d719951bd6133479f4e52041bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403590d719951bd6133479f4e52041bc.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecb078103edfb5a93e8b6af14166fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3ef4881bd7c5860178dbdbc7bba6e3.png)
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解答题-证明题
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【推荐1】已知,AB是⊙O的直径,BC是⊙O的弦,⊙O的割线PDE垂直于AB于点F,交BC于点G,∠A=∠BCP.
(1)求证:PC是⊙O的切线;
(2)若点C在劣弧AD上运动,其条件不变,问应再具备什么条件可使结论BG2=BF·BO成立,(要求画出示意图并说明理由).
(1)求证:PC是⊙O的切线;
(2)若点C在劣弧AD上运动,其条件不变,问应再具备什么条件可使结论BG2=BF·BO成立,(要求画出示意图并说明理由).
![](https://img.xkw.com/dksih/QBM/2018/4/1/1914916328669184/1918472032002048/STEM/8002ff2c201b44cf9079f09e58c92032.png?resizew=184)
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【推荐2】已知:
是
的直径,C为
上一点,将
绕着点B逆时针旋转一定的角度得到
,
交
于E点,若点D在
上,连接
交
于点F.
与
的位置关系;
(2)求证:
;
(3)若
,
,求阴影部分的面积.
![](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/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e59617707e98c3441445392333b491.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6823a329628699619a39cde927510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4297fd1f6b4a90ec1ea2c003356812a.png)
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解答题-计算题
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名校
【推荐1】如图,矩形
中,
,点P,Q分别在
上(均不含端点),且
点E,将
平移得到
,点P与点Q对应,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/1/d7d3b8e9-d3ee-4bff-9757-7ef6afb9fe2b.png?resizew=317)
(1)计算
________;当
时,求
的长,
(2)尝试 ①若
,求x的值;
②当
时,求点F到
的距离(用含x的式子表示).
(3)探究 连接
,若点P为
的中点,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ba94cec6c03980be9ca03774379fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60565b82dc19617af630daccc970f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a666403569e607f32af5f762c246dc7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/1/d7d3b8e9-d3ee-4bff-9757-7ef6afb9fe2b.png?resizew=317)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
(2)尝试 ①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc250adeb96d1a71e3171f7c857a2789.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b94f151c00959a1cd3946e7f8405337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)探究 连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
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解答题-问答题
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【推荐2】为方便调查森林树木的生长情况,林业工人用两把带刻度的直尺制作了一种叫做“角卡”的工具测量树干直径(如图1).如图2,3,4,两把直尺的
刻度为公共点M,夹角为
,利用两把直尺与树干横截面的公共点所对应的刻度值推测直径d的值.
相切于点A,B.
①若
,
,求直径d的值;(参考数据:
,
,
)
②若
,求
的值.
(2)如图3,4,
,树干横截面被切割成一个弓形.图3中,角卡与弓形的弦
两端接触,
;图4中,角卡一边与点D接触,另一边与弓形相切于点E,
,
.则在图3与图4中,利用哪个图的测量数据可以推测弓形所在圆的直径d?请指出是哪个图,并求d的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7bc87dabffb46d619bb3cfe79d9c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6089721ff03fe38254ab03fd99ef1272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c9d38be397849f71d24a97acf7d73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25996c789bb423811b2321d2516faa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4ff168c3f85e4b167c9ec68328640d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29f1faec31fdfca57b8a8d393667206.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae5e0514c4551c3905de4f25a3ee39a.png)
(2)如图3,4,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d41c0309086e62e7872c7057ae67585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6ab469448b43551c1ca599f719e9b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4745e8238f6162670b4fa57c4af676a9.png)
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