Using proportions, it is found that the radian measure of the central angle is given as follows:
[tex]\frac{4\pi}{3}[/tex] radians.
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The entire circumference is equivalent to a central angle of [tex]2\pi[/tex] radians. Hence the radian measure of the central angle considering two-thirds of the circumference is given as follows:
[tex]\frac{2}{3} \times 2\pi = \frac{4\pi}{3}[/tex]
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