彼が嘘をついているのは明らかだ。
It's obvious that he is lying.
明らかに間違いがある。
There is clearly a mistake.
Rare, mostly literary or archaic use for physical brightness. Modern Japanese normally uses 明るい for this meaning.
古い詩では「明らかな月」のように使われることがある。
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.