Chords AB and CD intersect at point E. Find CD if AE = 4 cm, BE = 9cm, and the length of CE is 4 times longer than the length DE.

Let the length DE = X cm, then, by condition, the length of the segment CE = 4 * X cm.

By the property of intersecting chords of a circle, the product of segments formed at the intersection of chords of one chord is equal to the product of segments of another chord.

DE * CE = AE * BE.

X * 4 * X = 4 * 9.

4 * X ^ 2 = 36

X ^ 2 = 36/4 = 9.

X = DE = 3 cm, then CE = 4 * 3 = 12 cm.

CD = DE + CE = 3 + 12 = 15 cm.

Answer: The length of the CD segment is 15 cm.