Question

A
120°
O
C
The circle has center O, and the measure of angle AOC is 120°. The
length of minor arc AC is what fraction of the circumference of the circle?
(The number of degrees of arc in a circle is 360.)

Answer 1

Answer:

The length of the minor arc AC is one-third of the circumference of the circle.

Step-by-step explanation:

To find the fraction of the circumference that the length of minor arc AC represents, you can follow these steps:

1. Calculate the circumference of the circle using the formula C = 2πr, where r is the radius of the circle.

2. Since the angle AOC is 120°, the measure of the minor arc AC is also 120° (since they intercept the same arc).

3. To find the length of the minor arc AC, you can use the formula: arc length = (angle/360) * circumference of the circle.

4. Substitute the values: arc length = (120/360) * 2πr = (1/3) * 2πr = 2πr/3.

5. Now, you have the length of the minor arc AC as 2πr/3.

6. To find the fraction of the circumference that the length of minor arc AC represents, you divide the length of the minor arc AC by the circumference of the circle: (2πr/3) / (2πr) = 1/3.

Therefore, the length of the minor arc AC is one-third of the circumference of the circle.