Arc cd is 1/4 of the circumference of a circle

Asked by wiki @ 12/07/2022 in Mathematics viewed by 177 People

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?

Answered by wiki @ 12/07/2022

Answer:

$\frac{\pi}{2}$ radians

Step-by-step explanation:

We can use the concept of proportion to answer this question.

The arc CD is given to be 1/4 in measure of the circumference of the circle. A complete circle is 360 degrees in measure which in radian measure is 2π

So, the arc which 1/4 in measure of the circumference will make an angle which is 1/4 of the angle of the entire circle.

i.e.

Angle formed by the arc = $\frac{1}{4} \times 2 \pi =\frac{\pi}{2}$ radians

Therefore, the radian measure of the central angle of arc CD is $\frac{\pi}{2}$ radians

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