Variations: by many contributors, whose names can be viewed by clicking "Page Info" at the bottom.
White captures three to make an eye. Black can't protect there because of shortage of liberties.
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.
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.
Blocking here is not sente: Black can take time to hane. White can't makes an eye in the corner because a and b are miai for Black.
If at b then at a and there are only false eyes in the corner.