Answer:
[tex]\frac{4}{3}\pi \: radians[/tex]
StartFraction 4 pi Over 3 EndFraction radians
Step-by-step explanation:
Arc CD is Two-thirds of the circumference of a circle.
[tex] \frac{central \: angle}{360} \times 2\pi \: r = \frac{2}{3} \times 2\pi \: r[/tex]
Divide both sides by 2πr
[tex] \frac{central \: angle}{360} = \frac{2}{3} [/tex]
In radians, since 360⁰ = 2π radians
[tex]\frac{central \: angle}{2\pi} = \frac{2}{3} [/tex]
3 × central angle = 2 × 2π
Divide both sides by 3
central angle = 4π / 3 rad
[tex]central \: angle = \frac{4}{3}\pi \: radians[/tex]
Answer:
[tex]\textsf{C)}\quad \dfrac{4\pi}{3}[/tex]
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle that subtends the arc.
Since angles around a point sum to 2π radians, the sum of the arcs of a circle is also 2π radians.
If arc CD is two-thirds of the circumference of a circle, then the measure of the central angle is two-thirds of 2π:
[tex]\dfrac{2}{3} \cdot 2\pi \\\\\\ \dfrac{4\pi}{3}[/tex]
So the radian measure of the central angle is:
[tex]\LARGE\boxed{\boxed{\dfrac{4\pi}{3}}}[/tex]
