题目

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．   答案：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．                                                                                                        

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