12-13九年级上·北京·期末
1 . 已知:如图,
是⊙O的直径,点
是
上任意一点,过点
作弦
点
是
上任一点,连结
交
于
连结AC、CF、BD、OD.
![](https://img.xkw.com/dksih/QBM/2012/2/8/1573338137673728/1573338344144896/STEM/0f904abfd388402eb48423134029ba92.png?resizew=131)
(1)求证:
;
(2)猜想:
与
的数量关系,并证明你的猜想;
(3)试探究:当点
位于何处时,△
的面积与△
的面积之比为1:2?并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743d2692ed78d7c0b0ec9a9dcc0c2da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df252f5ed1327337731a15b7f539ee5.png)
![](https://img.xkw.com/dksih/QBM/2012/2/8/1573338137673728/1573338344144896/STEM/0f904abfd388402eb48423134029ba92.png?resizew=131)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6b6666ef7b2cb418c9e9d3a2691d70.png)
(2)猜想:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86504cb5919fa932a58efc809a975d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5f2f61b4b2d0462dba55bdb4767af4.png)
(3)试探究:当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564743a1fe463a981f06914e3cb5e03e.png)
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12-13九年级上·北京丰台·期末
2 . 在Rt△ABC中,∠ACB=90
,AC=BC,CD⊥AB于点D,点E为AC边上一点,连接BE交CD于点F,过点E作EG⊥BE交AB于点G,
(1)如图1,当点E为AC中点时,线段EF与EG的数量关系是 ;
(2)如图2,当
,探究线段EF与EG的数量关系并且证明;
(3)如图3,当
,线段EF与EG的数量关系是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750e3df8d632555ebae34af74520cd2e.png)
(1)如图1,当点E为AC中点时,线段EF与EG的数量关系是 ;
(2)如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea66fded0a42fb50ad49f912e689d3b1.png)
(3)如图3,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ca8f0091eca99e6e4a6943c969ad3.png)
![](https://img.xkw.com/dksih/QBM/2012/1/20/1573331542843392/null/STEM/862be9aa481041f4b17fe69caa2e107f.png?resizew=554)
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2011·河南·中考模拟
3 . 如图,抛物线
经过
的三个点,已知
轴,点
在
轴上,点
在
轴上,且
.
(1)求抛物线的对称轴;
(2)写出
三点的坐标并求抛物线的解析式;
(3)探究:若点
是抛物线对称轴上且在
轴下方的动点,是否存在
是等腰三角形?若存在,请在图中画出所有符合条件的P点,然后直接写出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d6ae9fb3cfd2197edda07991de16d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecf1dfdce520f7d6895024f941304b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c287bb15494297df234f700f9f3a90d4.png)
(1)求抛物线的对称轴;
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378a2df371f5ff1815c03a84f571229.png)
(3)探究:若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703b40a6293ed9e33001e2919379b168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2011/10/14/1573262243381248/1573262298251264/STEM/cbc8e7b0b7ff482a8743b0d280a41c75.png?resizew=192)
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2011·四川乐山·中考真题
真题
4 . .如图(1),在直角△ABC中, ∠ACB=90
,CD⊥AB,垂足为D,点E在AC上,BE交CD于点G,EF⊥BE交AB于点F,若AC=mBC,CE=nEA(m,n为实数).
试探究线段EF与EG的数量关系.
![](https://img.xkw.com/dksih/QBM/2011/8/10/1573240342773760/1573240425308160/STEM/2a0ebaf8c4ff4f6a87e0f6b689dc9af3.png)
(1)如图(2),当m=1,n=1时,EF与EG的数量关系是
证明:
(2) 如图(3),当m=1,n为任意实数时,EF与EG的数量关系是
证明
(3)如图(1),当m,n均为任意实数时,EF与EG的数量关系是
(写出关系式,不必证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc39661fd9aa55f1e7089e5924709a56.png)
试探究线段EF与EG的数量关系.
![](https://img.xkw.com/dksih/QBM/2011/8/10/1573240342773760/1573240425308160/STEM/2a0ebaf8c4ff4f6a87e0f6b689dc9af3.png)
(1)如图(2),当m=1,n=1时,EF与EG的数量关系是
证明:
(2) 如图(3),当m=1,n为任意实数时,EF与EG的数量关系是
证明
(3)如图(1),当m,n均为任意实数时,EF与EG的数量关系是
(写出关系式,不必证明)
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