彼が嘘をついているのは明らかだ。
It's obvious that he is lying.
There is clearly a mistake.
Rare, mostly literary or archaic use for physical brightness. Modern Japanese normally uses 明るい for this meaning.
In old poetry, it is sometimes used like 'a bright moon'.
There was an obvious contradiction in his explanation.
He was clearly tired.
It is clear that he is the culprit.
明らか means 'clear/obvious' and is typically used affirmatively, whereas 定か stresses certainty and is almost always used in negative contexts.