(2003•泰州)已知:如图,⊙O与⊙O
1内切于点A,AO是⊙O
1的直径,⊙O的弦AC交⊙O
1于点B,弦DF经过点B且垂直于OC,垂足为点E.
(1)求证:DF与⊙O
1相切;
(2)求证:2AB
2=AD•AF;
(3)若AB=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232441953884086/SYS201310212324419538840003_ST/0.png)
,cos∠DBA=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232441953884086/SYS201310212324419538840003_ST/1.png)
,求AF和AD的长.
考点分析:
相关试题推荐
(2003•黄石)如图,过Rt△ABC的直角顶点C作圆O,圆O与△ABC的两边AB、BC分别相切于D、C,并交AC边于E.在优弧DE上任取一点F,连接FE、FD,若BC=a,cos∠EFD=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232441953884086/SYS201310212324419538840002_ST/0.png)
.
①求证:AD=BD;
②试求∠EDA的大小;
③计算圆O的面积.
查看答案
(2003•随州)已知,⊙O与直线l相切于点C,直径AB∥l,P是l上C点左边(不包括C点)一动点,AP交⊙O于D,BP交⊙O于E,DE的延长线交l于F.
(1)当PC<AO时,如图1,线段PF与FC的大小关系是______.结合图1,证明你的结论;
(2)当PC>AO时,AP的反向延长线交⊙O于D,其它条件不变,如图2,(1)中所得结论是否仍然成立?
答:______;(不证明)
(3)如图2,当tan∠APB=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232441953884086/SYS201310212324419538840001_ST/0.png)
,tan∠ABE=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232441953884086/SYS201310212324419538840001_ST/1.png)
,AP=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232441953884086/SYS201310212324419538840001_ST/2.png)
时,求PF的长.
查看答案
(2003•十堰)如图,ABCD为菱形,∠ABC=β,有一个半径为r的⊙O,圆心O在菱形的内部,且到B点的距离为a,当圆心O在菱形内部运动时,⊙O的半径和圆心到B点的距离a都发生变化.
(1)当满足什么条件时,圆心O在菱形内部运动时⊙O与菱形的两边BA、BC(或BA、BC的延长线)都相切?
(2)当圆心O在菱形内部运动时,请你求出满足什么条件时⊙O与菱形的两边BA、BC(或BA、BC的延长线)都相交、相离的所有情况.
查看答案
(2003•贵阳)如图,已知AB为⊙O的直径,AC为弦,OD∥BC,交AC于D,BC=4cm.
(1)求证:AC⊥OD;
(2)求OD的长;
(3)若2sinA-1=0,求⊙O的直径.
查看答案
(2003•杭州)如图,⊙C经过原点且与两坐标轴分别交于A、B两点,点A的坐标是(0,4),M是圆上一点,∠BMO=120°,求⊙C的半径和圆心C的坐标.
查看答案