Question

two circles, b and e, have different radii but share the same central angle, θ. how does the similarity of these circles help establish a relationship between their intercepted arc lengths and radii? since the two circles, b and e, are similar, the ratio of the arc lengths is the same as the ratio of the radii. since the two circles, b and e, are similar, their intercepted arcs are equal, regardless of the radius. since the two circles, b and e, are similar, the arc lengths are proportional to the square of the radii. since the two circles, b and e, are similar, the ratio of arc length to radius remains constant across all circles.

Explanation:

For similar circles with the same central - angle, the ratio of the arc length \(s\) to the radius \(r\) is equal to the central - angle \(\theta\) (in radians), i.e., \(s = r\theta\). So, the ratio of arc length to radius is the same (equal to the central - angle \(\theta\)) for similar circles with the same central - angle.

Answer:

Since the two circles, \(B\) and \(E\), are similar, the ratio of arc length to radius remains constant across all circles.