作∠A的平分线AD交BC于D,过D作DE⊥AB于E,
∵∠A=2∠B,∴∠CAD=∠DAB=∠B =>AD=DB,又DE⊥AB =>AE=EB=1/2AB=AC
∴△ADC≌△ADE(SAS) =>∠ACD=∠AED=90°