European Girls Math Olympiad 2021 P3 - A simply complex geometry problem with a couple of tricks

For this problem you only need to know about similarity and the power of point as a bare minimum. Experience is a big plus here because most solutions require some level of creativity or ingenuity. More advanced techniques can be useful.

[reshmikuntichandra]

Thank you for the amazing content! Keep uploadin' we need these

[andreben]

Wow this one's harder. Part of what I found difficult was finding ways of having a clear figure that could contain everything and not be messy, especially since there's so much angle chasing involved. I tried using geogebra (which actually allowed me to find that A, E, F, N, M were co-cyclic even before I knew of point P) but OH MY GOD there so many lines I couldn't see anything XD

I really loved the second solution a lot more since it didn't use the trigonometric Ceva (which I have never heard of XD), but somehow I just lacked the patience to push it and find my own solution :(

I guess I'm not as strong a geometer as I thought 😅