Sum of Segment Lengths in Circle

In a circle with a radius of 6 units, two chords, AB and CD, intersect at point E. The lengths of the segments are given as follows: AE = 3 units, EB = x units, CE = 2 units, and ED = y units. The measure of angle AEC is 60°.

Find the sum of the lengths of segments EB and ED, representing the total distance from point E to points B and D.

You can use the intersecting chord theorem: if two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord, i.e., AE × EB = CE × ED.