证明：∵PA是圆O的切线∴∠PAB=∠C∵PF平分∠APB∴∠APE=∠CPF∵∠AEF=∠PAB+∠APE，∠AFE=∠C+∠CPF∴∠AEF=∠AFE∴AE=AF∵M是弧BC的中点∴∠BAM=∠CAM∴AM⊥EF即AM⊥PF
