[milesde]

Hi! I wrote that proof back in 2007, half of my lifetime ago. It's neat to see it discussed again.

My original writeup was longer and included several of the details that you mentioned. However, the editors of the American Mathematical Monthly condensed it, presumably so that it could be published as a "filler" that would take up less than a page. What you see is their rewrite of my work.

In fairness to them, the stuff that's left out is well known to people who think about incircles and excircles and thus not really new. For instance, it's used in the proof of Heron's formula by similar triangles.

There were some things that I would not have put that way on my own. For instance, at that point in my life, I had actually been trained not to use the word "clearly" like it's used here.

But who was I, a high school student, to quibble with the editors of the American Mathematical Monthly? I was thrilled that they wanted to publish my work. No regrets.

[bonzini]

Hey it's nice that you found this post and replied! You shouldn't have any regrets indeed, and I guess that style has its place for a "filler" article, even though calling it a filler is not so nice...

Make it a rant about the editors—if they had been your "mistakes" they should have corrected you, and I am happy to learn that they weren't yours in the first place.