If the intersection of AO extends to point f, then AF is the diameter, angle ABF=90 degrees, and arc AB corresponds to angles BFA and BCA, so

Angle BFA=BCA, and because angle ADC=ABF=90 degrees, angle BAF=DAC, and e is the midpoint of arc BC, so

Angle BAE=CAE, BAE-BAF=CAE-CAD, so angle EAO=EAD.