[squeakynick]

Any path that is not straight could have been reached sooner by going on the straight line connecting: The shortest distance between two opposite corners on a rectangle is the diagonal line between them. Any curve you draw connecting them is longer. Any curved path you run gets you to the same point later than you could have got to it at if you went directly there. Outside of the circle of safety, it has to be a straight path.

A spiral is also not going to work outside the circle of safety, as the monster has a higher angular velocity; he moves around the shore faster than your projection to the shore.