Xuanxuan Qijing Problem 51 / Solution

Black's resistance  

is necessary to secure enough eye space.

After the space at 'x' is rendered useless, because of the atari at 'a'.

 

So the shape in the previous diagram is practically the same as this one; the group is dead.

If black tries to play 'a', white makes an eye in the corner with 'b' and wins the capturing race.

Failure

 

results in ko, which is not the best here.

On the other hand, if black has outside liberties, this the best white can do.

 

first is similar to the previous diagram.

 

For other , makes life.