In the latest column reprint, how about including the diagram of the problem Cecil’s trying to solve? I know it was there for the books.
Yeah, it’s scarcely worth reprinting without the image.
BigT provided an image in this previous thread. Geometry problem Jan. 4, 1991 - Cecil's Columns/Staff Reports - Straight Dope Message Board
Cecil knows fuck all about gometry.
Then he matches your facility with spelling, I guess.
Powers &8^]
F-
Show your work!
No Cecil’s geometry is correct at least I assume since without the diagram, I don’t know where to go after step 8. Fortunately, there is no need to go past step 8. Here’s why. At step 8, he claims, correctly, that angle XCE = angle YCE. But that implies that E is on the angle bisector of angle ACE (= angle XCY). But it is well known that the three angle bisectors meet in a point*, so D is on the angle bisector.
- Why? The angle bisector of the angle at A (i.e. CAB) consists of all points equidistant from AC and AB and the bisector at B consists of the points equidistant from AB and BC. But then D is also equidistant from AC and BC.
Looking back on my previous post, I realize that the proof that E lies on the angle bisector of the angle at C is exactly the same as the proof that D does. In fact, E is equidistant from CA (extended) and CB since it is equidistant from CA and AB and also from CB and AB, hence from AC and BC and that is the same argument for D. Of course, it is well known that the three interior angle bisectors meet at a point; the fact adduced here less known.
I wish to withdraw my comment. As Powers and John W. Kennedy point out I am plainly wrong and Cecil is one of the great minds of modern gometry. Either that or he knows fuck nothing about it.
don’t ask was attempting to call attention to the OP’s misspelling.
Unsuccessfully, I guess. 
Yes, I apologize to don’t ask. I didn’t catch the reference.
Powers &8^]
I did indeed, but it’s on a server that keeps having problems, so I’ll repost it.
Hopefully this one will last longer. (The site was one of the first in Google results, so it should be popular.)
I’ve been staring at that drawing and working through Cecil’s column, and something is a little off on that drawing. Cecil says
Looking at the picture, those triangles clearly are not congruent. However, the problem statement says
That problem statement defines EB as the bisector of angle CBZ. Therefore, I have to conclude the drawing is not precise and work from the problem description, not the visual appearance. Doing so, Cecil’s proof works out.
So for anyone playing at home, the point labels are correct and give a visual correlation for the description, but don’t rely on the appearance of the triangles. It was probably a quick sketch, not a precise bisection.