圆内接四边形若有一组邻边相等,则称之为等邻边圆内接四边形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/5d3c0d33-59ed-4ac1-bfe5-f9baa0077d41.png?resizew=375)
(1)如图1,四边形
为等邻边圆内接四边形,
,
,直接写出
的度数;
(2)如图2,四边形
内接于
,
为
的直径,
,
,若四边形
为等邻边圆内接四边形,
,求
的长.
(3)如图3,四边形
为等邻边圆内接四边形,
,
为
的直径,且
.设
,四边形
的周长为
,试确定
与
的函数关系式,并求出
的最大值.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/5d3c0d33-59ed-4ac1-bfe5-f9baa0077d41.png?resizew=375)
(1)如图1,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246a86f34603eaf2e6a948681b831b0d.png)
(2)如图2,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae33911e41aa2f7004cc01e336f96bf0.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/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae33911e41aa2f7004cc01e336f96bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff29971ccc633d89832ffa9bd54afa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)如图3,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a16dc02090b6e9263555061f14fbc8c.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/cdf7a191ebf8bc6ad30137e001d18be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa41f80c6e33393a9f7bb57fca6b493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
更新时间:2024-01-05 12:01:00
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相似题推荐
解答题-问答题
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适中
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名校
【推荐1】如图,在圆内接四边形
中,
若四边形
的面积是S,
的长是x.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/635445d2-1716-49e4-aead-11dab413869d.png?resizew=144)
(1)求
的度数;
(2)求S与x之间的函数关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c605b56913b2ef12b18b1160512fe45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/635445d2-1716-49e4-aead-11dab413869d.png?resizew=144)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
(2)求S与x之间的函数关系式.
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【推荐2】如图,正方形
的边长是4.E是
边上一点(E不与A、B重合),F是
的延长线上一点,
.四边形
是矩形,其面积
随
的长
的变化而变化且构成函数.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/efab2ff1-d70b-4958-89fa-5c46256cde8b.png?resizew=176)
(1)求
与
之间的函数关系式,并写出自变量
的取值范围;
(2)若上述(1)中是二次函数,请用配方法把它转化成
的形式,并指出当
取何值时,
取得最大(或最小)值,该值是多少?
(3)求出抛物线与
轴的交点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5774f580a6bb0cd5291cd8d14e2af648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a528a9e05c1097f568566ceac619ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/efab2ff1-d70b-4958-89fa-5c46256cde8b.png?resizew=176)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若上述(1)中是二次函数,请用配方法把它转化成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcff1114aa1a7d118ccbeec937a55c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(3)求出抛物线与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐1】已知:如图,圆O是等腰△ABC的外接圆,AB=AC,AB=10,CD=
BC,tanD=
.求:
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742572268969984/2743033223806976/STEM/f3fdeffbbbae4331a0b7ddd6f6dd4ceb.png?resizew=195)
(1)线段BC的长;
(2)圆O的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://img.xkw.com/dksih/QBM/2021/6/14/2742572268969984/2743033223806976/STEM/f3fdeffbbbae4331a0b7ddd6f6dd4ceb.png?resizew=195)
(1)线段BC的长;
(2)圆O的半径.
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【推荐2】(1)如图,已知:AB∥CD,BE⊥AD,垂足为点E,CF⊥AD,垂足为点F,并且AE=DF.求证:四边形BECF是平行四边形.
![](https://img.xkw.com/dksih/QBM/2015/6/3/1573845047320576/1573845053775872/STEM/7ee3046dda414ea3b84a633dbc545bbe.png)
(2)如图,AC是⊙O的直径,弦BD交AC于点E.①求证:△ADE∽△BCE;②如果
=AE·AC,求证:CD=CB
![](https://img.xkw.com/dksih/QBM/2015/6/3/1573845047320576/1573845053775872/STEM/7ee3046dda414ea3b84a633dbc545bbe.png)
(2)如图,AC是⊙O的直径,弦BD交AC于点E.①求证:△ADE∽△BCE;②如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d37b9bfc0e291952dc2004277fc3cc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/3/1573845047320576/1573845053775872/STEM/bbadb135493a494886ca36933a4a2468.png)
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【推荐1】如图1,四边形
内接于
,
为直径,过点
作
于点
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/6f344be6-5418-48df-ab4a-d0c8f16a6313.png?resizew=315)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cea68e55bcee57b1730ae469c4925e1.png)
(2)如图2,连接
,若
是
的切线,
.请判断四边形
的形状,并说明理由.
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f913298f0fae9f55377a8deab9f099dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/6f344be6-5418-48df-ab4a-d0c8f16a6313.png?resizew=315)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cea68e55bcee57b1730ae469c4925e1.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65639672f444b3d4dc6fc4f357ddbd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607543bb9f55b8a141ed2d6cf0e1a20b.png)
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【推荐2】如图,在△ABC和△ADE中,∠BAC=∠DAE=90°,AB=AC,AD=AE,连接BD、CE.
(1)求证:BD=CE;
(2)若延长BD交CE于F,求∠AFB的度数.
(1)求证:BD=CE;
(2)若延长BD交CE于F,求∠AFB的度数.
![](https://img.xkw.com/dksih/QBM/2020/10/27/2579913603178496/2580829918748672/STEM/067c542b0aaa46c7ae33d854310319fb.png?resizew=276)
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