To determine the radian measure of the central angle corresponding to arc CD, we need to understand the relationship between the arc length and the central angle.
Given:
- Arc CD is [tex]\(\frac{1}{4}\)[/tex] of the circumference of the circle.
First, recall that the circumference of a circle is given by [tex]\(C = 2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius. The entire circumference corresponds to a central angle of [tex]\(2\pi\)[/tex] radians.
Since arc CD is [tex]\(\frac{1}{4}\)[/tex] of the circumference, the central angle corresponding to arc CD will be [tex]\(\frac{1}{4}\)[/tex] of [tex]\(2\pi\)[/tex] radians.
To find this angle, we calculate:
[tex]\[ \text{Central angle} = \frac{1}{4} \times 2\pi \][/tex]
By simplifying the product:
[tex]\[ \text{Central angle} = \frac{1}{4} \times 2\pi = \frac{2\pi}{4} = \frac{\pi}{2} \][/tex]
Therefore, the radian measure of the central angle is:
[tex]\[ \boxed{\frac{\pi}{2}} \][/tex]
