To derive the fact that the length of the arc of a circle intercepted by an angle is proportional to the radius of the circle. what should the arc length first be compared to?

a. the circumference
b. a chord
c. the area
d. the diameter

1 answer

To derive the fact that the length of the arc of a circle intercepted by an angle is proportional to the radius of the circle, the arc length should first be compared to:

a. the circumference

The reasoning is that the arc length can be expressed as a fraction of the total circumference of the circle, which is directly related to the angle subtended at the center of the circle and the radius. The comparison helps establish the proportionality between the arc length and the radius when considering angles in radians.