The chords AB and CD meet at point E. Find CD if AE = 4cm, BE = 9cm and CE is 4 times the length of DE.

Let DE = x cm, then CE = 4x cm (since, according to the problem statement, the CE length is 4 times the DE length).

By the property of intersecting chords, we get:

AE * EB = CE * ED.

Let’s substitute the data we have:

4 * 9 = 4x * x.

Let’s simplify the resulting expression:

36 = 4 x ^ 2;

we express x ^ 2:

x ^ 2 = 36/4;

x ^ 2 = 9;

x = 3.

CD = CE + ED = 4x + x = 5x. Substitute the found value instead of x and get: CD = 5 * 3 = 15.

Answer: 15 cm.