(2002•湛江)已知:如图,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
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909021_ST/0.png)
上运动,其他条件不变,问应再具备什么条件可使结论BG
2=BF•BO成立?(要求画出示意图并说明理由)
(3)在满足问题(2)的条件下,你还能推出哪些形如BG
2=BF•BO的正确结论?(要求:不再标注其他字母,找结论的过程中所作的辅助线不能出现在结论中,不写推理过程,写出不包括BG
2=BF•BO的7个结论)
考点分析:
相关试题推荐
(2002•浙江)如图,⊙O′经过⊙O的圆心,E、F是两圆的交点,直线OO′交⊙O′于点P,交EF于点C,交⊙O于点Q,且EF=2
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909020_ST/0.png)
,sin∠P=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909020_ST/1.png)
.
(1)求证:PE是⊙O的切线;
(2)求⊙O和⊙O′的半径的长;
(3)若点A在劣弧
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909020_ST/2.png)
上运动(与点Q、F不重合),连接PA交劣弧
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909020_ST/3.png)
于点B,连接BC并延长交⊙O于点G,设CG=x,PA=y,求y关于x的函数关系式,并写出自变量x的取值范围.
查看答案
(2004•日照)如图,AB是⊙O的直径,点P在BA的延长线上,弦CD⊥AB于点E,∠POC=∠PCE.
(1)求证:PC是⊙O的切线;
(2)若OE:EA=1:2,PA=6,求⊙O的半径;
(3)求sin∠PCA的值.
查看答案
(2002•滨州)如图,在Rt△ABC中,∠ACB=90°,AC<BC,以AC直径的⊙O交AB于D,∠B的平分线分别交AC、CD于E、F.
(1)求证:CE=CF;
(2)若BC=6,AD=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909018_ST/0.png)
,求BD的长;
(3)求sinA的值.
查看答案
(2002•朝阳区)已知:在内角不确定的△ABC中,AB=AC,点E、F分别在AB、AC上,EF∥BC,平行移动EF,如果梯形EBCF有内切圆.
当
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/0.png)
时,sinB=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/1.png)
;
当
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/2.png)
时,sinB=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/3.png)
(提示:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/4.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/5.png)
);
当
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/6.png)
时,sinB=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/7.png)
.
(1)请你根据以上所反映的规律,填空:当
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909017_ST/8.png)
时,sinB的值等于______
查看答案
(2002•崇文区)已知:如图,PA切⊙O于点A,割线PBC交⊙O于点B、C,PD⊥AB于点D,PD、AO的延长线相交于点E,连接CE并延长CE交⊙O于点F,连接AF.
(1)求证:△PBD∽△PEC;
(2)若AB=12,tan∠EAF=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702890932/SYS201310212325577028909016_ST/0.png)
,求⊙O半径的长.
查看答案