can you tell me the differences between the words "obvious", "apparent" and "evident"?

I assume that you have looked at the various meanings in the dictionary for these words, so I won't explain all of those.

Instead, I'll just comment briefly on these simple examples.

Tom says to me, 'The answer is obvious'.  

This sometimes suggests that Tom thinks I am a bit stupid for not seeing the answer.

Despite this, 'obvious' is the most common word of the three.

Tom says to me, 'The answer is apparent'.  

This is a more neutral way to say it.

Tom says to me, 'The answer is evident'.  

This suggests that Tom is a person who likes to speak precisely.

Best wishes, Clive