Could anyone tell what I'm missing?
I know that angle trisection is proven to be impossible (see Pierre Wantzel in https://en.wikipedia.org/wiki/Angle_trisection). However, I just came up with the following method and can't find any flaw
Steps (sorry, I'm not super precise describing it)
- Given angle ABC
- draw a circle from point B, to intersect both angle lines in U and L points
- join created points to get line segment UL
- multiply the segment 3 (since it's trisection) times on one of angle line (creating points L1, L2, L3 or U1, U2, U3 depends on which line you pick)
- draw a line crossing L3 & U points (or U3 & L)
- draw a parallel line that crosses L2 and UL in point X1
- draw a parallel line that crosses L2 and UL in point X2
- draw one line crossing points B & X1
- draw one line crossing points B & X2
Now the angle ABC should be divided into 3 equal angles?
You can also watch quick presentation/draft with computer program.
https://odysee.com/@xliiv:f/trisect-angle-with-tales:2
Perhaps, here's the reason why the method is false, but can't catch it https://en.wikipedia.org/wiki/Intercept_theorem#Algebraic_formulation_of_compass_and_ruler_constructions