Beginner Exercise 270 / Solution

Solution  

makes an immediate eye while threatening to lasso the two white stones. After connects, lives. (In practice, should connect at a.)

Variation  

atari just backfires. The forced captures White in connect and die - at a is a self-atari.

Failure  

Atari at is a fatal mistake. White plays hane. Due to shortage of liberties, Black can't play at a.

Failure continued ( at )  

So captures, then captures back the stone. Black is left with only one eye.