一、<h2 align=left >选择题(本大题共 10小题,每小题 4 分,共 40 分。)</h2>
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1.
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的值等于( )
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2.
下列事件中是随机事件的是( )
A . 通常加热到100℃时,水沸腾
B . 在只装有黑球和白球的袋子里,摸出红球
C . 购买一张彩票,中奖
D . 太阳从东方升起
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3.
已知⊙O的半径为1cm,点D到圆心O的距离为2cm,则点D与⊙O的位置关系是( )
A . 点D在⊙O外
B . 点D在⊙O上
C . 点D在⊙O内
D . 不能确定
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4.
某正方体的平面展开图如图所示,由此可知,原正方体“中”字所在面的对面的汉字是( )
![](//tikupic.21cnjy.com/2020/11/23/1179ec65f53168bb1e19dee264802287.png)
A . 国
B . 的
C . 中
D . 梦
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5.
如图, DE∥BC ,若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmi%3EE%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则△ADE与四边形BCED的面积的比是( )
![](//tikupic.21cnjy.com/2020/11/23/886a4dbf0607b6e4b70f395de3f88cac.png)
A . 1:9
B . 1:8
C . 1:6
D . 1:3
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6.
如图,▱ABCD的顶点A,B,D在⊙O上,顶点C在⊙O的直径BE上,∠ADC=54°,连接AE,则∠AEB的度数为(
)
![](//tikupic.21cnjy.com/2020/11/23/e70dcc256997ff55a529bf4b1365b11e.png)
A . 36°
B . 46°
C . 27°
D . 63°
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7.
如图,AC⊥BC,AC=BC=4,以AC为直径作半圆,圆心为点O;以点C为圆心,BC为半径作弧AB.过点O作BC的平行线交两弧于点D、E,则阴影部分的面积是( )
![](//tikupic.21cnjy.com/2020/12/05/7f4d52566d39f2798beaaf16b55f87fe.png)
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8.
如图,Rt△ABC中,∠C=90°,AC=3,BC=4,点P为AB上的一个动点,过点P画PD⊥AC于点D,PE⊥BC于点E,当点P由A向B移动时,四边形CDPE周长的变化情况是( )
![](//tikupic.21cnjy.com/2020/11/23/f1badd750624881a683cc57fa243b271.png)
A . 逐渐变小
B . 逐渐变大
C . 先变大后变小
D . 不变
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9.
如图,AC,BC是两个半圆的直径,∠ACP=30°,若AB=2a,则 PQ的值为(
)
![](//tikupic.21cnjy.com/2020/11/23/7e3d8371ec4cb0962d5bc4b5b2c7cd81.png)
A . a
B . 1.5a
C .
D .
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10.
(2019·余姚会考)
如图,四张大小不一的正方形纸片分别放置于矩形的四个角落,其中,①和②纸片既不重叠也无空隙.在矩形ABCD的周长已知的情况下,知道下列哪个正方形的边长,就可以求得阴影部分的周长( )
![](//tikupic.21cnjy.com/2020/11/23/976beb843a611c7b21b757d0d2ffb9ea.png)
A . ①
B . ②
C . ③
D . ④
二、填空题(本大题共6小题,每小题5分,共30分)
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12.
把抛物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
向左平移1个单位,然后向下平移3个单位,则平移后抛物线的解析式为
.
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13.
如图,△
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
中,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E90%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,斜边
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
上一点
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmath%3E)
,使得
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则
.
![](//tikupic.21cnjy.com/2020/11/23/8e1e059ac87224682148e63c6eaf7e95.png)
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14.
如图,已知AB∥CD∥EF,AD∶AF=3∶5,BE=12,那么CE的长等于
.
![](//tikupic.21cnjy.com/2020/11/23/b92ba05b2ec25fc6bd7d3d4e3f1d9b33.png)
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15.
直线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
和
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
在同一直角坐标系中的图象如图所示,则抛物线
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的对称轴为
![](//tikupic.21cnjy.com/2020/11/23/7a35714e63c8ed2798a18e575b442a55.png)
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16.
如图,在矩形纸片ABCD中,已知AB=1,BC=
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,点E在边CD上移动,连接AE,将多边形ABCE沿AE折叠,得到多边形AB'C'E,点B、C的对应点分别为点B'、C'.当点E从点C移动到点D的过程中,点C'移动的路径长为
.
![](//tikupic.21cnjy.com/2020/11/23/9c6a0df8210bdf61fda8bb8956537db8.png)
三、解答题(本大题有 8 小题,其中第17——19题各8分;第20——22题各10分;第23题12分,第24题14分,共80分.)
-
17.
计算:
-
(1)
-
(2)
已知
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%E2%89%A0%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,求代数式
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%C2%B7%3C%2Fmo%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的值
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18.
如图,△ABC是正方形网格图中的格点三角形(顶点在格点上),请分别在图1和图2的正方形网格内按下列要求画出格点三角形.
![](//tikupic.21cnjy.com/2020/11/23/31291ea736d66db3ffee66b2584b1ccb.png)
-
(1)
在图1中,画△DEF与△ABC相似,且相似比为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
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(2)
在图2中,画△PQR与△ABC相似,且相似比为
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsqrt%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
.
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19.
如图,有四张背面完全相同的纸牌A、B、C、D,其正面分别画有四个不同的几何图形,这四张纸牌背面朝上洗匀.
![](//tikupic.21cnjy.com/2020/11/23/f7d3722304201327be381090aa2741b2.jpg)
-
(1)
从中随机摸出一张,求摸出的牌面图形是中心对称图形的概率.
-
(2)
小明和小亮约定做一个游戏,其规则如下:先由小明随机摸出一张纸牌,不放回,再由小亮从剩下的纸牌中随机摸出一张,若摸出的两张牌面图形都是轴对称图形,则小明获胜,否则小亮获胜,这个游戏公平吗?请用列表或画树状图的方法说明.(纸牌用A、B、C、D)
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20.
如图,从观察点A处发现北偏东45°方向,距离为9海里的B处有一走私船。这时一艘缉私艇位于A点的北偏西53°方向的C处,且C点恰好在B点的正西方向。此时走私船正以每小时50海里的速度从B处向北偏东30°方向逃窜,缉私艇奉命立即以每小时50 海里的速度向走私船追去。
![](//tikupic.21cnjy.com/2020/11/23/219198a3595cd0aee77a70e698002005.jpg)
-
-
(2)
缉私艇沿什么方向行驶,才能在最短时间内追上走私船?并求出所需时间.(参考数据:sin53º≈0.8,cos53º≈0.6,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Etan%3C%2Fmi%3E%3Cmn%3E53%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3Cmo%3E%E2%89%88%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
)
-
21.
已知二次函数
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的图象经过点(1,0)和(0,2).
-
-
(2)
当
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%89%A4%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
时,求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmath%3E)
的取值范围;
-
(3)
已经点P(m,n)在该函数的图象上,且
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,求点P的坐标.
-
22.
如图,在Rt△ABC中,点O在斜边AB上,以O为圆心,OB为半径作圆,分别与BC,AB相交于点D,E,连结AD.已知∠CAD=∠B.
![](//tikupic.21cnjy.com/2020/11/23/92028bae6cca651c17cebccb7299d990.jpg)
-
-
(2)
若BC=8,tanB=
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmath%3E)
, 求⊙O的半径.
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23.
若抛物线的顶点到
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴的距离与抛物线截
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴所得的距离相等,则称该抛物线是等距抛物线.
![](//tikupic.21cnjy.com/2020/11/23/617aa06b1b8c4714af2746f4d5b748c2.png)
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(1)
判断:二次函数
(填“是”或“不是”)等距抛物线;
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(3)
在(2)的条件下,若该抛物线与
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E)
轴交于A,B两点(点A在点B的左侧),顶点为C,在此抛物线上是否存在一个点F,使得∠FAB=∠ACB. 若存在,请求出点F的坐标;若不存在,请说明理由.
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24.
如图1.已知⊙M与x轴交于A、B两点,与y轴交于C、D两点,A、B两点的横坐标分别为﹣1和7,弦AB的弦心距MN为3,
![](//tikupic.21cnjy.com/2020/11/23/2d8f28b79aebb1af943602e06aed4c02.jpg)
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(3)
如图2,P在弦CD上,且CP=2,Q是弧BC上一动点,PQ交直径CF于点E,当∠CPQ=∠CQD时,求CQ的长;
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(4)
如图3.若P点是弦CD上一动点,Q是弧BC上一动点,PQ交直径CF于点E,当∠CPQ与∠CQD互余时,求△PEM面积的最大值.