Question

如圖，已知點(diǎn)A（0，1），B（0，﹣1），以點(diǎn)A為圓心，AB為半徑作圓，交x軸的正半軸于點(diǎn)C，則∠BAC等于　　　　　　度．                                                                       

                                                                       

Answer 1

　60　                                                                                              

【考點(diǎn)】垂徑定理；坐標(biāo)與圖形性質(zhì)；等邊三角形的判定與性質(zhì)；勾股定理．                    

【分析】求出OA、AC，通過余弦函數(shù)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°，                                                                                  

故答案為60．                                                                                    

【點(diǎn)評】本題考查了垂徑定理的應(yīng)用，關(guān)鍵是求出AC、OA的長．