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Black can live by playing on the 1-2 point as shown.
Other possible defenses end up in ko or seki, depending on black's choice, as the next two diagrams show.
Yes, white still can kill. After 7 - Bent four in the corner
The extra hane gives a sense of security.
The key tesuji here is .
The best moves by both players lead to a ten-thousand year ko.
Black can also get a multi step ko (for white) sequence, which should be better than ten-thousand year ko.
Black can get rid of ko threats before continuing. If white wants to continue, he must play yet another ko to force the atari.
Only now does the real ko for the life of the corner start. Black usually should be able to win this or receive ample compensation elsewhere in the steps white took.
Now the 2-2 point is the vital point for Black.
The hane at may seem to give some help in living.
To kill, can go straight to the 2-2 point. After , Black is dead. See the addendum of the rectangular six in the corner page. Study: Would the marked White stone still be needed if the Black hane was at the top?
The two hane stones give some degree of security.
The second L+1 group with a weak leg is also unsettled. White can kill at a or Black can live by playing at a.