Something is messed up in these circle questions you're presenting. You are descibing two intersecting diameters, AD and BC, that form vertical angles at the center of circle O.
If angle BOA = 40 degrees, then angle DOC = 40 degrees because vertical angles have equal measures.
That would make arc CD = 40 degrees since the measure of a central angle is the same as its subtended arc. But you said arc CD = 70 degrees, and that's not possible.