如图，已知CD是△ABC中AB边上的高，以CD为直径的⊙O分别交CA、CB于点E

如图，已知CD是△ABC中AB边上的高，以CD为直径的⊙O分别交CA、CB于点E、F，点G是AD的中点．求证：GE是⊙O的切线．

证明：（证法一）连接．            

∵是⊙O的直径，

．                                           

∵是的中点，

．                                                  

．                                                                                                                     

∵．                                                                                                 

．即．                                                        

是⊙O的切线．                                                                                                        

（证法二）连接．                                       

∵，

．                                                            

．                                             

∵OC=OE．

∴∠2=∠4．                                                               

∴∠1=∠3．                                                               

又，

．                                                                                                      

．                                                                                               

是⊙O的切线．