Before long you will be 1/4 of the radius away from the center and the tiger will be 180 degrees away. At this point swim straight to the point on the shore furthest from the tiger. You will be able to get there in 3/4 units of time, while it will take the tiger pi/4 =~ 0.7854 units of time.

Thanks to 'Bob' for this one.

Michael Shackleford, A.S.A., 11/27/1998