Fun and games at the circus

See if you can outrun the lions and solve this puzzle from St John’s Maths Tutor Dr David Seifert…

Imagine the following two-player video game. One player takes the role of a moody circus lion, the other plays its nimble tamer. Both players are confined to the circus arena, which has unit radius, and we think of both the lion and the tamer as points in the mathematical sense rather than spatially extended objects. As the game is about to begin the lion is performing a trick at the centre of the arena and the lion tamer stands at a safe distance of 0.5 from the lion. The lion’s mood suddenly turns, and the game begins. Now both players move at the same constant speed in a direction of their choice. The lion’s aim is to capture the lion tamer, the lion tamer’s aim is to escape for as long as possible.

Does either player have a winning strategy? That is to say, is there a strategy for the lion which guarantees capture, or is there a strategy for the lion tamer which guarantees indefinite survival?