If at here, cutting at makes miai of a and b. Note that if White sacrifices just one stone ( at c), it's a ko after at a. :
If here, capturing three stones with assures a quiet life. Even if Black throws in at , White is alive with a and b being miai.
Giving atari this way would not be very smart. White now captures either at a or at b.
at . The variation is long, but up until in this diagram it is forced and the - exchange is well known. White has to find the throw-in at , though.
We will have a look at some preparatory moves: why White should not yet start the well-known sequence.
If a has not yet been exchanged for b, White runs out of options. Whatever she does, Black will connect at c.
If at b then at a and there are only false eyes in the corner.