Let us use the property of intersecting chords, according to which the product of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.
AE * BE = CE * DE.
DE = AE * BE / CE = 4 * 9/12 = 36/12 = 3 cm.
Answer: The length of the segment DE is 3 cm.
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