Spoiler for doubting Ogre gives up so quick
It is a lot simpler than that for the zen master Ogre. The Ogre ignores where the maiden looks, where she goes, and where she intends to go. Ogre simply draws an imaginary straight line from the center of the lake, through the boat, to the shore; and heads for that spot using the shorter arch. Insofar as the optimum is concerned, it is the Ogre who determines the path -- not the maiden. The maiden reacts to Ogre's moves, not other way around.
If the maiden wanders back into her inner circle r, that could make the Ogre change the direction when the boat crosses straight line drawn from the Ogre to the center of the lake. Then the young lady would be going towards Ogre rather than away from him. (Not an optimal strategy.)
Presently, we are solving the sub-problem, where the maiden after leaving her inner circle goes in a straight line towards some point on the shore. We must find, that point. Bonanova suggested going off the inner circle on a tangent line. That gives a better ratio than going in a straight line to the nearest point on the shore. However, I don't believe it is the optimum.
The numbers I have given in the post #23 inside the spoiler are off. But then, as everyone knows, I am siding with Ogre.
Blame it on the cold, Prime.
I am not convinced that tangential is optimal - it may not be enough!
It's easy to overlook that r is one of the unknowns.
I did overlook that r is one of the unknowns because of cold and my partiality to Ogre's cause.
Still I don't see that the problem is solved even for a straight line escape.
By the way, I did not see the answer by Phaze to which you referred. Is BD not displaying some of the posts to me?
Good catch Prime, and I have no health excuse. Apologies.
I've edited my post 25 to properly attribute you as the solver.
We can't continue indefinitely increasing the angle however.
At some point it will become to the ogre's advantage to reverse his direction.
Edited by bonanova, 22 February 2013 - 05:56 AM.
Add final statement