Question

如图，已知点A（0，1），B（0，﹣1），以点A为圆心，AB为半径作圆，交x轴的正半轴于点C，则∠BAC等于　　　　　　度．                                                                       

                                                                       

Answer 1

　60　                                                                                              

【考点】垂径定理；坐标与图形性质；等边三角形的判定与性质；勾股定理．                    

【分析】求出OA、AC，通过余弦函数即可得出答案．                                   

【解答】解：∵A（0，1），B（0，﹣1），                                            

∴AB=2，OA=1，                                                                               

∴AC=2，                                                                                          

在Rt△AOC中，cos∠BAC==，                                                        

∴∠BAC=60°，                                                                                  

故答案为60．                                                                                    

【点评】本题考查了垂径定理的应用，关键是求出AC、OA的长．