Now from D draw DC at right angles to AB, and meeting the lawn at C. You can do that with a hoe.
Produce CD to meet the lawn again at E.
Now we do some more of that bisecting; this time we bisect EC at F.
Then F shall be the middle of the bed; and that's where your rose-tree is going.
Proof???—Well, I mean, if F be not the centre let some point G, outside the line CE, be the centre and put the confounded tree there. And, what's more, you can jolly well join GA, GD and GB, and see what that looks like.
Just cast your eye over the two triangles GDA and GDB.
Don't you see that DA is equal to DB (unless, of course, you've bisected that chord all wrong), and DG is common, and GA is equal to GB—at least according to your absurd theory about G it is, since they must be both radii. Radii indeed! Look at them. Ha, ha!
Therefore, you fool, the angle GDA is equal to the angle GDB.
Therefore they are both right angles.
Therefore the angle GDA is a right angle. (I know you think I'm repeating myself, but you'll see what I'm getting at in a minute.)