Question

如圖，BD為⊙O的直徑，AB=AC，AD交BC于點E．

1.①求證：△ABE∽△ADB；②若AE=2，ED=4，求⊙O的面積

2.延長DB到F，使得，連接FA，若AC∥FD，試判斷直線FA與⊙O的位置關系，并說明理由．

 

Answer 1

 

1.

2.直線FA與⊙O相切

解析:(1) ① AB=AC∠ABC=∠ADC

                 ∠BAD=∠BAE

                 △ABE∽△ADB

              ②△ABE∽△ADB

                 

                  AB=

                  BD為⊙O的直徑

                  △ADB是直角三角形

                   BD==

                  S==.

          (2) 直線FA與⊙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°

               直線FA與⊙O相切