Chords AB and CD intersect at point M. Find the length of chord AB if CM = 4 cm, DM = 9 cm, AM: MB = 4: 1.

By the property of intersecting chords of a circle, the product of the segments of one chord formed by the intersection point is equal to the product of the segments of the other chord.

Let the length of the segment BM = X cm, then, by condition, the length of the segment AM = 4 * X cm.

AM * BM = CM * DM.

4 * X * X = 4 * 9.

4 * X ^ 2 = 36.

X ^ 2 = 9.

X = BM = 3 cm.

AM = 4 * 3 = 12 cm.

Chord length AB = AM + BM = 12 + 3 = 15 cm.

Answer: The length of the chord AB is 15 cm.