Run away from lions in a cage

It seems so that this is related to the optimization theory problem The Lion and Man and is in general a pursuit problem.

Peter

I would hope to avoid being cornered (metaphorically speaking) and try to get on a path that passes through the middle. The lions on the other hand, being team workers, would want to get to a position where they could home in for the kill. I see it going pretty much like this:

Initially we are all heading towards H, after a long chase in which the lions have just failed to catch me. At around the centre, the lions sense they are not going to catch me in a straight line, but notice the edge of the ring is not too far off, so they instinctively start to spread out along the paths CL.

The lions are just about to start homing in for the kill when I scupper their plans by doing an about turn towards J. Thinking that they have a chance to catch me they home in the other way towards the point E where they think they might get their meal.

Luckily I just avoid being eaten because I have a laser measuring device and a calculator with me.

So my conclusion is that the ratio of my speed to the lions needs to be slightly greater than HE:LE which would presumably be dependent on the diameter of the ring.