CEMC Hypatia, 2006

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, $\triangle ABE$ , $\triangle BCE$ and $\triangle CDE$ are right-angled, with $\angle AEB = \angle BEC = \angle CED = 60^\circ$ , and $AE = 24$ .

(a) Determine the length of $CE$ .

(b) Determine the perimeter of quadrilateral $ABCD$ .

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