Ptolemy's Riddle III

Geometry Level 2

A cyclic quadrilateral \(ABCD\) is constructed within a circle such that \(AB = 3, BC = 6,\) and \(\triangle ACD\) is equilateral, as shown to the right.

If \(E\) is the intersection point of both diagonals of \(ABCD\), what is the length of \(ED,\) the blue line segment in the diagram?

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