Gokyo Shumyo, Section 1, Problem 83 / Solution

Main line  

Variation ^[1] discusses @ .

Continuation  

makes a first eye, a and b being miai. threatens to kill the corner in a capturing race: see variation ^[2]. Hence connects. makes the second eye. If she omits it, Black at c or destroys the second eye.

variation 1  

If at here, White wins the capturing race. Losing four moves with a to d, she still has 7 liberties left to attack, while Black has only three to defend (he'll have to react to one).

Variation 2  

a to f are theoretically Black's semeai liberties (he's on the defence), but to c or d (atari) and a (two eyes) he has to react, which leaves him with 4 liberties. White has already 6 at the circled points (minus g to connect) so she clearly wins the race.