Help!

In the diagram, triangle ABE, triangle BCE and triangle CDE are right-angled, with Angle AEB= Angle BEC= Angle CED=60 degrees, and AE=24. Find the length of CE.

\(\overline{BE}=\overline{AE}\cdot cos\ 60\ degrees\\ \overline{BE}=24\cdot cos\ 60\ degrees=24\cdot 0.5=12\\ \overline{CE}=\overline{BE}\cdot cos\ 60\ degrees\\ \overline{CE}=12\cdot cos\ 60\ degrees=12\cdot 0.5=6\\ \)

\(\overline{CE}=6 \)

until the end

[\(\overline{DE}=\overline{CE}\cdot cos\ 60\ degrees\\ \overline{DE}=6\cdot cos\ 60\ degrees=6\cdot 0.5=3\\ \color{blue}\overline{DE}=3\)

  !

ΔABE  ~ Δ BEC   which implies that

AB/ BE = BE / EC

And  ΔABE   is a 30 - 60 - 90 right triangle....AE  = 24  and BE  = 1/2 of this  = 12

So

24 / 12  = 12 / EC

12 /6  = 12 / EC

EC   =  CE  = 6