连接OE,交AB于G,连接OF,交AC于H ∵OE⊥AB,OF⊥AC,∴∠EGA=∠FHA=90°,∵OE=OF,∴∠OEF=∠OFE,∴∠AMN=∠EMB=180°-∠EGA-∠OEF=180°-∠FHA-OFE=∠FNC=∠ANM.