The problem presents a circle with center $O$ and a diameter $A B$. We are asked to compare the measure of angle ACB (Quantity A) with $90^{\circ}$ (Quantity B).

The key piece of information, as clarified, is that Point C is NOT on the circumference of the circle. This is critical because it changes the geometric rule that applies.

Geometric Principle:
1. If the vertex of an angle ( C ) lies on the circumference of a circle and subtends the diameter (AB): The angle is always a right angle, i.e., $\(90^{\circ}\)$. (This is the "angle in a semicircle" theorem).
2. If the vertex of an angle $(\mathrm{C})$ lies inside the circle and subtends the diameter $\((\mathrm{AB})\)$ : The angle will always be obtuse, meaning its measure is greater than $\(90^{\circ}\)$.
3. If the vertex of an angle ( C ) lies outside the circle and subtends the diameter ( AB ): The angle will always be acute, meaning its measure is less than $\(90^{\circ}\)$.

Applying the Information:
Given that the official answer states Quantity A is greater than Quantity B, this implies that Measure of angle ACB > 90 .
For this to be true, according to the geometric principles above, point C must be located inside the circle.

Even though the diagram might visually suggest C is on the circumference (a common drawing convention), the problem's implicit (or now explicit) condition that C is not on the circle, combined with the answer being Quantity A is greater, forces the conclusion that C is an interior point.

Comparison:
- Quantity A: Measure of angle ACB. Since C is inside the circle and subtends the diameter AB, Measure of angle ACB > 90.
- Quantity B: $\(90^{\circ}\)$

Since Quantity A is greater than $90^{\circ}$, it is clearly greater than Quantity B.

The final answer is Quantity A is greater