> I just did a 5-minute check with Geometer's Sketchpad. In one >iteration (original directions only) it didn't do too well. My angle >was 75 degrees. My guess for placing D was BD/BA=0.292. >The angle E'OB comes out to be 25.562 degrees, 2% high. > I think my construction is correct because as the first guess >approaches 25 degrees, the construction result does also. > But I agree that further tweaks might make it much better.
I think there is something wrong with your construction. I am assuming you were using 75 degrees as your unknown angle at point A,(this is the original lettering), intended length AB=AC=1 and the first guess radius from step 4 to be CD=.292 (I'm not sure why you call it BD). My results using the above yield 24.996 deg. Even if I do use BD=.292, (which is outside the first guess parameters of the construction) I get 25.174 deg.