Final answer:
The measure of an arc intercepted by a central angle, like angle C, is equal to the angle itself in degrees. Over small segments, arc length can be approximated as the straight-line distance. For exact arc length, use the formula involving the radius and central angle in radians.
Step-by-step explanation:
In the context of circle geometry, the measure of the arc intercepted by angle C is directly related to the angle itself when C is located at the center of the circle. Since CD is the perpendicular bisector of segment AB, angle C is central, and thus, the measure of arc AB is equal to the measure of angle C in degrees. In scenarios where arc lengths are considered over small portions of a circle, the arc length can be approximated to the straight-line distance between the endpoints of the arc. Additionally, the proportionality between the degrees in an arc and the total 360 degrees in a circle can be used to find the corresponding arc length, given the circle's radius.
To compute the exact arc length, one could use the formula arc length (As) = radius (r) × central angle (A) in radians. However, if angle C is given in degrees, you would first need to convert to radians by multiplying by \(\pi/180\). For example, if C is 60 degrees and the circle has a radius r, the arc length is r × (\(\pi/3\)). Understanding these concepts is essential for solving problems related to circle geometry and related arc measures.