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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)

  1. Given angle ABC
  2. draw a circle from point B, to intersect both angle lines in U and L points
  3. join created points to get line segment UL
  4. 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)
  5. draw a line crossing L3 & U points (or U3 & L)
  6. draw a parallel line that crosses L2 and UL in point X1
  7. draw a parallel line that crosses L2 and UL in point X2
  8. draw one line crossing points B & X1
  9. 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

xliiv
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    It looks like you are trisecting a chord. Note that to trisect the angle, you should really trisect the arc of the circle instead. – NDB Aug 15 '23 at 18:53
  • @xliiv NDB is correct. The reason your trisection doesn't work is because the relationship between a chord and its corresponding arc is not a linear one. – H. sapiens rex Aug 15 '23 at 23:03
  • NDB, H.sapiensrex you're right. Now i understand the reason and difference, so you have answered my question. Thank you! – xliiv Aug 16 '23 at 16:22

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