But then again, there's an error in the proof of IMO P3, in Fig1.f and Step 26. of the full proof in supplimentary material[1], which it states that ∠GMD = ∠GO2D, which is incorrect. It should be ∠GMD + ∠GO2D = π. I am trying to follow its logic but I cannot parse Step 25. Did it hallucinate this step?

It has the right idea of O2 being on the nine point circle though.

edit: I retract my statement. It looks like it is using directed angles[2] which then the statement becomes correct.

[1]: https://storage.googleapis.com/deepmind-media/DeepMind.com/B...

[2]: https://web.evanchen.cc/handouts/Directed-Angles/Directed-An...