A duck and fox - interesting problem!

[kate]

A duck is in the middle of a lake with a form of a circumference (i.e. in the center of the circumference). The fox, which cannot swim is watching the duck from the shore, in order to eat it. If the duck flies away - it saves itself. But the duck cannot fly away from the water - it has to be on the ground in order to fly away. The question is with what relationship between the maximum speed of running of the fox on the ground and maximum speed of swimming of the duck in the water, the duck has no chance to save itself?