Final answer:
The value of AB is equal to the value of BC because BD is the perpendicular bisector of segment AC.
Step-by-step explanation:
In this problem, we are given that BD is the perpendicular bisector of segment AC. To find the value of AB, we need to understand that the perpendicular bisector cuts the segment AC into two equal halves. So, we can conclude that AB is equal to BC. Therefore, the value of AB is equal to the value of BC.