Question

如图，BD为⊙O的直径，AB=AC，AD交BC于点E．

1.①求证：△ABE∽△ADB；②若AE=2，ED=4，求⊙O的面积

2.延长DB到F，使得，连接FA，若AC∥FD，试判断直线FA与⊙O的位置关系，并说明理由．

 

Answer 1

 

1.

2.直线FA与⊙O相切

解析:(1) ① AB=AC∠ABC=∠ADC

                 ∠BAD=∠BAE

                 △ABE∽△ADB

              ②△ABE∽△ADB

                 

                  AB=

                  BD为⊙O的直径

                  △ADB是直角三角形

                   BD==

                  S==.

          (2) 直线FA与⊙O相切。

             AC∥FD

             ∠BDA=∠CBD

            ∠BDA=∠CBD=∠ABC

            ∠BDA=30°

            ∠BOA=60°

             BO=AO,BF=BO

            AB=FO

              △AOF是直角三角形，

              ∠0AF=90°

               直线FA与⊙O相切