1. Let's clarify the problem: We are dealing with a circle where $AC$ is a segment related to the circle. 2. If $AC$ is a diameter, then its length is twice the radius. So if the radius is $r$, then $AC = 2r$. 3. If $AC$ is given as 10, then the radius $r = \frac{AC}{2} = \frac{10}{2} = 5$. 4. If you thought $AC$ was a radius, then its length should be 5, not 10. 5. The key point: The diameter is the longest chord passing through the center, so if $AC$ passes through the center, it is the diameter. 6. Therefore, if $AC$ is the diameter, its length is 10, and the radius is half of that, 5. 7. If you are asked to find the length of $AC$ and it is the diameter, you set it equal to 10, not 5. 8. Summary: $AC$ is diameter $\Rightarrow AC = 2r = 10$, so $r = 5$. If $AC$ were radius, then $AC = 5$.