Olympiad Geometry Problem #32: IMO 2019 #6

This is a very difficult geometry problem. It was the last problem (#6) of the International Math Olympiad in 2019. Hope you all enjoy, would love to hear your thoughts!

[박준언-jp]

After watching this video, I became very interested in Casey's theorem. Can you make a video proving this theorem please?

[michaelgreenberg]

I made a few small mistakes in the video - see if you can find them :)

[alekseyovchenkov]

i study in Russia and i was taught a lot of geometry stuff including tricky and hard technics liek poles and polars, isogonal conjugate and etc, but no one ever told me about Casey's theorem! I think it can be useful when need to prove something lies on radical axis, so thank you)

[asmaehiba]

It's really hard to get the solution.

[browse]

There is an easier solution using spiral similarly