证：∵AC平分∠MAN又由∠ABC=角ADC=90°知CD⊥AM,CB⊥AN∴CD=CB在△CAD和△CAB中 CA=CACD=CB∴△CAD≌△CAB（HL）∴AD=AB,∠DAC=∠BAC,∠DCA=∠BCA又 ∠MAN=120°∴∠DAC=∠BAC=60°∴∠DCA=∠BCA=30°∴DA=BA=1/2AC...