Now the white 5 stones on the left are weak, so black wants to attack white.
However, the cut at A is always worrying for black.
Even if white doesn’t cut now, white can make use of it later to gain some advantage.
However, black has a good move here to indirectly protect against the cut.
Protecting at 1 or A or B is definitely not a bad move.
However, it’s not sente so white can run the few stones freely at 2.
Black can also go further by peeping at 1.
However, white can get 2 and 4 in sente and come out at 6.
Protecting the cut will just allow white to come out, so black needs to think of something.
One thing to take note is that the white 4 stones here are actually weak with the liberties quite tight.
If black can threaten to take these 4 stones, then black does not need to worry about the cut at A anymore.
But what can black do here?
Atari at 1 is a feel-good exchange, but it doesn’t really do anything.
Black still has to worry about the cut.
Throw-in here is a common tesuji in this situation.
If white answers at A, black can throw-in again at B to make a ko.
However…
White can answer here to avoid the ko.
If black atari at A white will just take at B and black can’t really do anything in the corner.
The correct move is to cut on the other side here and see how white answers.
If white answers here, then now A becomes an atari and black can start the ko.
However, the beauty of this is that black need not start the ko immediately.
Just this exchange alone already lowered the severity of the cut.
Black can play from 3 to 9 to strengthen itself first before attacking white at 11.
If white tries to cut here, black can throw-in at 2 to make a ko and win the ko using the ko threats at A etc.
Black has effectively protected the cut by threatening the white 4 stones with a ko.
All these was achieved with the exchange of B and C.
What if white tries to avoid the ko by connecting here?
Locally, it seems like a good move.
However…
Due to the special situation in the corner, black playing at 1 and cutting at 3 is a good move.
Answering here will be a disastrous result for white as black cuts the 2 stones on the outside.
Answering here is also not good. Once black gets the atari at 2, black can hane at 4. Now white has no choice to play at A and start the ko, but this is a much heavier ko for white.
Another thing to take note is that if you play here first, white will get the atari at 3.
Now the cut at 5 doesn’t work anymore.
Now white can connect here.
Even you play 2 and 4, white can atari at 5 now because the atari at A is already protected.
That is the reason why cutting at 1 now is the best timing.
In fact, you can say it’s the only timing. Any later and it may not work.
White can’t connect at A but white can’t tenuki either, so white can only answer at 2.
This effectively deters the cut at B and black can get sente to attack the centre white group more freely.
This is why I consider B4 to be a beautiful move :).