Chord BD and CE intersect at point A, with AC = 6 cm, AE = 12 cm, AB 1 cm less than AD. find BD.

Let AB = x, then AD = x + 1
The product of the segments of chords intersecting at one point is a constant value:
CA * AE = BA * AD
6 * 12 = x * (x + 1)
We solve the equation:
x (x + 1) = 72
x ^ 2 + x-72 = 0
D = 289
x1 = (- 1 + 17) / 2 = 8
x2 is not taken into account, because its value is negative, which does not satisfy the condition of the problem.
AB = 8 (cm)
АD = 1 + 8 = 9 (cm)
BD = 8 + 9 = 17 (cm)
Answer: 17cm