The Predator and the Prey puzzle

[Pri6 / Sec2 Maths: Circles] Hey, here's a brainteaser for you:

A prey is floating in the middle of a circular lake. A predator is prowling around the bank. The predator can run four times faster than the prey can swim, and the predator, hungry as it is, will always position itself in the best possible spot on the side of the lake to catch the (insert prey here).

The prey can only escape safely from dry land. So, is there a way for the prey to reach the side of the lake, and run / fly to safety - without being caught by the predator?

Some simple understanding of a circle's properties, as well as the ability to apply / manipulate ratios is all you require to solve this puzzle. Do you think you can find the answer?