I'm playing 'b' without much more thought. If black wants to take 'c' and give up a second move on the left then I'm all in. 'b' certainly looks bigger than 'a' unless I'm missing a clever play.

Black's lower left group is in danger. If White can kill it then White has a won game. Or at least if somehow Black manages to live in gote then White can take the big point "c" later. In addition, Black's central group doesn't have so much space to live and White has an entry thanks to N6 so even though Black won't die in the center, White will have a good endgame by threatening to kill.

If White plays "a" then Black can save part of his group, which is not small. Then maybe Black can reduce with by threatening to rescue the two stones.

Click Here To Show Diagram Code

[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O X . . . . . . . . . . . . . . |
$$ | . . . O X . . . . . . . . . . . c . . |
$$ | . . O X . X . . . X . . . . . X . . . |
$$ | . . O X . . . . . . . . X . . . . . . |
$$ | . . O . . . . . . . . . . . X X . . . |
$$ | . . . . 6 . . . . O . O . O . O X . . |
$$ | . . . . . . . . O . . . . O . O X . . |
$$ | . . . . . . O . O X X . X X . O . . . |
$$ | . . . , . . . O X , . . . . . , . . . |
$$ | . . . . . X . O X . . . . X . O . . . |
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . O . 5 X . O . . . . . . X X O O X . |
$$ | . . O 4 3 1 . X . . . . O O O X X X . |
$$ | . . . X . . 2 . . X X . . . . O O X . |
$$ | . . O , X X . O . O . . . . . O X . . |
$$ | . . . O O X . . . . . O . X O O X . . |
$$ | . . . . . . . O . . . . . . O X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

If White plays "b" then I don't see a way for Black to make an eye around that point. Here is a crude variation:

Click Here To Show Diagram Code

[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O X . . . . . . . . . . . . . . |
$$ | . . . O X . . . . . . . . . . . c . . |
$$ | . . O X . X . . . X . . . . . X . . . |
$$ | . . O X . . . . . . . . X . . . . . . |
$$ | . . O . . . . . . . . . . . X X . . . |
$$ | . . . . . . . . . O . O . O . O X . . |
$$ | . . . . . . . . O . . . . O . O X . . |
$$ | . . . . . . O . O X X . X X . O . . . |
$$ | . . . , . . . O X , . . . . . , . . . |
$$ | . . . . . X . O X . . . . X . O . . . |
$$ | . . . . . . . O X . . . . . . . . . . |
$$ | . O . . X . O . . . . . . X X O O X . |
$$ | . . O 5 6 4 1 X . . . . O O O X X X . |
$$ | . . . X . 8 2 3 . X X . . . . O O X . |
$$ | . . O 9 X X 7 O . O . . . . . O X . . |
$$ | . . . O O X . . . . . O . X O O X . . |
$$ | . . . . . . . O . . . . . . O X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

So it seems very difficult for Black to live, and as White I would try to kill.

b is my instinct, and looks best. I'd probably not even think of a in a game as flabby shape, but as mentioned looked for its pros which are is a cleaner threat to cut at d7. But why cut 1 stone when you can cut the whole e4 group which is unsettled, and middle too?
c doesn't even look like the right spot to invade top, is be thinking more to the left, looking for some p18 m17 combo. Actually with l14 sente maybe not.

The straight cut is best, the diagonal, smaller cut was my mistake. The third option was a distraction.