The Trinity and the Law of Non-Contradiction

Christian theology has to come up with a way to signal and clarify. To say that God is three persons in one being is not a violation of the law of non-contradiction. It's not for instance saying God is a square circle because it's actually impossible to be a square circle. So I'm all for a very limited use of analogies. For instance, how is the son from the father? Oh, kind of like heat and light come from the solar disk without leaving it.