Herman: is the obvious first move, as otherwise Black's group will be cut in two by a white move there. Simply living with part of the group with a Black move at a is not sufficient.
If white decides to save the stone with , then lives. But here white is being too easy on black.
The obvious counter-attack for white is to play the vital point with . If black defends with , then prevents an eye in the center, and Black dies on a large scale.
Therefore, black should make the eye in the center. White then spoils Black's eyeshape with . threatens to make an eye in the corner, which prevents. then guarantees a second eye.
Instead white can play and to capture three stones and get some points in the corner. In exchange, makes Black's group alive.