OK, so Black has to play and kill White. The five moves that pop into my head are:
a: Which will connect the two stones there, so they can't be split, also if we can prevent White from making another eye, we can kill her (since her only eyespace will be almost filled with an unsettled three)
b: If White plays here, she already has half an eye (though black can start a ko by capturing at c), so the idea is to play on this key point to foil White.
c: Capturing White's stone here might be a good idea, but if White plays b he'll have to connect, or start a ko.
d: This prevents White from playing a and splitting the stones apart, however it'll need some reinforcement in a turn or two.
e: Not a very good move (I think). White can just respond with d. It does reduce White's eyespace by one, though, so if the above possibilities don't pan out, we'll try this.
Reconsidering, I think that d and e are the best possible moves. If Black doesn't play d or e, then White can connect her two groups (which are connected now by a knight's jump).
Read below to figure out the answer along with me, or just jump to /Solution.
First let's look at what happens if White doesn't reinforce her stone at the marked space. Black can capture it with 3, but it's not a very good situation for him, since White reponds with 4 and Black is dead inside. (If Black connects his groups, White will have enough eye space, and if Black doesn't connect, White will fill in liberties and then play at the marked space taking Black and gaining two eyes.)
If Black plays at b, White tries to split the black stones apart with 2. If Black responds by taking the stone in the corner, White plays 4 at 3 killing Black and gaining two eyes. So Black reinforces at 3, but White seals him in at 4.
After Black's stones are taken by 6, even Black 7 can't kill the white group. Even if 5 and 9 were played at the circles (putting the L-shaped white group on the left in atari) 10 still saves her.
If Black captures the stone at the marked space with 1, White will respond with 2. A black connection at the marked space is useless, so he plays 3 instead.
White retakes with 4. Black would like to take White's group of three (the unit containing 2), but unless he reinforces at 5, White will take his marked stone. White blocks at 6, which seals the black group in. If White plays z next time, Black will die.
Black is forced to play the ko at 7. White responds at 8 and Black is dead. Also, White's two chains each have two liberties, so there's no way Black can kill them in time.
When Black plays 1, White must respond with 2, because if she allowed Black to play there, he would split her group apart.
Black then captures White's stone with 3. White would like very much to play at the marked space, so that she can take 1 and chip away at Black's structure, but if she played there, she'd put that chain in atari. However, White 4 connects her groups, so Black 3 isn't really that good.
So, let's play Black 3 to block the connection. White 4 is the natural choice. Black plays 5 to save his stone, and White plays 6.
Black plays threatening to take White's entire left group, and White plays , capturing two stones. White is alive.
Ok, let's try yet another position for Black 3. We'll keep White 4 where it is. White can't play at the marked space, so she'll have to approach from either y or z, at which time Black plays at the marked space and almost fills White's eyespace with a bulky five.
Can White avoid this fate?
No matter where White plays 4, Black can always play 5.
(See /solution for some more variations.)
To see what happens if Black plays e:
Black 1 at e. If White responds at 2, Black plays 3. (A white play at 3 connects her groups.) But White 4 ensures Black's death -- when Black captures with 5, he is killed in a snapback.
I was wondering what would happen in this following variation:
Thus, white's group is cut in two, and I don't see any plausible escape, except maybe crawling down on the left side, but, black would still have the advantage if it just chases, as it can develop greater influence toward the center.
xela: Actually, I think white can live via a double ko!