题目
题型:不详难度:来源:
![]() |
AB |
![]() |
AD |
![](http://img.shitiku.com.cn/uploads/allimg/20191107/20191107234255-16969.png)
答案
∵EA切⊙O于A,
∴∠EAB=∠ACB.
∵
![]() |
AB |
![]() |
AD |
∴∠ACD=∠ACB,AB=AD.
于是∠EAB=∠ACD.
又四边形ABCD内接于⊙O,
∴∠ABE=∠D.
∴△ABE∽△CDA.
于是
AB |
CD |
BE |
DA |
∴AB2=BE•CD.
![](http://img.shitiku.com.cn/uploads/allimg/20191107/20191107234255-29677.png)
核心考点
举一反三
如图,已知四边形ABCD内接于ΘO,且AB是的ΘO直径,过点D的ΘO的切线与BA的延长线交于点M.
(1)若MD=6,MB=12,求AB的长;
(2)若AM=AD,求∠DCB的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191107/20191107234251-47230.png)
![数学公式](http://img.shitiku.com.cn/uploads/allimg/20191107/20191107234246-57028.png)