The length of the segment AB is 15 cm, find the length of the segment CD if AD = 12cm and CB = 10cm.

In order to solve the problem, we first need to know the length of the segments AC and DB:

AC = AB – CB = 15 cm – 10 cm = 5 cm;

DB = AB – AD = 15 cm – 12 cm = 3 cm;

Now, to find out the length of the segment CD, we must subtract the sum of AC and DB from the length of the whole segment:

CD = AB – (AC + DB) = 15 cm – (5 cm + 3 cm) = 7 cm.

Answer: the length of the segment CD = 7 cm.