Answer: CB: 16, AB: 32 (units)
Explanation:
The question mentioned that the compass was set to the same width, indicating that any arc drawn from the same point will have same distance from its origin.
In this case, if can represent the intersection above the segment as D and the intersection below the segment as E and extend the points in a shape as:
Triangle ADE and
Triangle BDE.
Since they share the base,
and as the distance from
A to D,
A to E,
B to D,
and B to E
are same as mentioned above("the compass was set to the same width, indicating that any arc drawn from the same point will have same distance from its origin.")
We can conclude congruence between ADE and BDE.
Congruent triangles have identical shape and therefore same heights(AC and BC).
And therefore, line BC is 16 units and line AB is 32 units.