To solve this problem, we need to determine the size of angle ∠ACB using the given diagram.

Analysis:

1. O is the center of the circle, so AO, BO, and CO are radii of the circle.
2. Triangle $\triangle ABC$ is an isosceles triangle, as $OA = OB = OC$ (radii of the circle).
3. The central angle $\angle AOB$ subtends the arc $AB$. The inscribed angle $\angle ACB$ subtending the same arc is half of $\angle AOB$.

Relationship:

$\angle ACB = \frac{1}{2} \times \angle AOB$

To calculate $\angle ACB$, we need $\angle AOB$, which can be given or inferred. Let me know if the measure of $\angle AOB$ is provided, or if any additional details are available in the problem.

Would you like more clarification on the steps? Here are some related questions:

1. What is the specific measure of the central angle $\angle AOB$?
2. Why is the inscribed angle always half of the central angle subtending the same arc?
3. How does the circle theorem help in solving such problems?
4. Can this property apply to other inscribed angles in the same circle?
5. What are the key properties of isosceles triangles used here?

Tip: Always look for symmetry and key properties of circles, such as the relationships between radii, central angles, and inscribed angles!