2015-2016学年江西省抚州市崇仁二中九年级下第一次月考数学试卷含答案解析  
4．下列判断中正确的是（　　）                                                             
A．平分弦的直线垂直于弦                                                                       
B．平分弦的直线也必平分弦所对的两条弧                                               
C．弦的垂直平分线必平分弦所对的两条弧                                               
D．平分一条弧的直线必平分这条弧所对的弦                                           
【考点】垂径定理．                                                                           
【分析】根据垂径定理对各选项进行逐一判断即可．                                       
【解答】解：A、平分弦（非直径）的直径垂直于弦，故本选项错误；                   
B、平分弦的直径也必平分弦所对的两条弧，故本选项错误；                          
C、弦的垂直平分线必平分弦所对的两条弧，符合垂径定理，故本选项正确；               
D、平分一条弧的直径必平分这条弧所对的弦，故本选项错误．                      
故选：C．                                                                                          
【点评】本题考查的是垂径定理，熟知弦的垂直平分线平分弦、垂直于弦，平分弦所对的两条弧是解答此题的关键．