Please find the attachment for a better understanding of the answer.
As we can clearly see from the diagram, as the radius of the circle reduces so does the length of the arc for the same congruent angle subtended at the center.
Thus the length of the arc intercepted by a congruent central angle is proportional to the radius in similar circles.
This can be mathematically proven as thus:
Let be the length of the arc
Let theta be the central angle
Let r be the radius.
We know that =(theta)r
Therefore, for a constant theta, the arc length will vary in the same proportion as the radius.
