Paradoxes Break What?!?!

Only a short while ago I had a difficult time distinguishing between the Law of Non-Contradiction and the Law of Excluded Middle. I was trying to determine where the problem of a paradox fit into these laws and which one it breaks. Essentially, I have determined that these laws are essentially the same law, just stating opposite inflections. The Law of Excluded Middles basically states that a statement  must be either true OR false, it cannot be neither true nor false. The Law of Non-Contradiction states that a statement cannot be both true and false because, again, it must be on or the other. So, based on this, I think that paradox break the Law of Excluded Middle. I think that I have a proper understanding of this. If not, feel free to enlighten me.