To determine the radian measure of the central angle corresponding to arc CD, which is [tex]\(\frac{1}{4}\)[/tex] of the circumference of the circle, let's follow these steps:
1. Understand the relationship between the circumference and radians:
A complete circle measures [tex]\(2\pi\)[/tex] radians, which corresponds to the full circle's circumference.
2. Identify the portion of the circle represented by arc CD:
The problem states that arc CD constitutes [tex]\(\frac{1}{4}\)[/tex] of the entire circumference.
3. Calculate the central angle in radians:
Since the total measure of a full circle is [tex]\(2\pi\)[/tex] radians, the measure of the central angle for [tex]\(\frac{1}{4}\)[/tex] of the circumference is:
[tex]\[
\frac{1}{4} \times 2\pi = \frac{2\pi}{4} = \frac{\pi}{2} \text{ radians}
\][/tex]
Therefore, the radian measure of the central angle corresponding to arc CD is [tex]\(\frac{\pi}{2}\)[/tex] radians.
Among the provided options, the correct answer is:
[tex]\[
\frac{\pi}{2} \text{ radians}
\][/tex]
