Problem

[seephyro]

There is a circle with a devil upon the circle and a devil in the middle of the circle.
The devil moves in a constant velocity upon the circle, and the man can move freely inside the circle, with constant velocity, from the center, with the objective of exit from the circle without be eaten by the devil.
What is the maximum value of the quocient between the velocity of the devil and the velocity of the man in the middle, such that the devil cannot reach the man.

 

[stapel]

There is a circle with a devil upon the circle and a devil in the middle of the circle.

Is this supposed to read "and a man in the middle"?

The devil moves in a constant velocity upon the circle, and the man can move freely inside the circle, with constant velocity, from the center, with the objective of exit from the circle without be eaten by the devil.
What is the maximum value of the quocient between the velocity of the devil and the velocity of the man in the middle, such that the devil cannot reach the man.

What picture have you drawn? What variables have you defined? What equations have you set up? Where are you getting stuck?

Please be complete. Thank you!

 

[HallsofIvy]

Suppose the man turns directly away from the devil and runs to the circle. What distance does he have to cover to get out of the circle? What distance does the devil have to cover to catch him?