If segment AC is the diameter of the circle and AC = 21 cm, what is the length of arc AB? Use 3.14 for pi.

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Even assuming that the subject is geometry, we do not know what arc AB encompasses.

To find the length of arc AB, we need to know the measure of the central angle that corresponds to that arc.

To calculate the measure of the central angle, we can use the fact that a central angle intercepts the same arc length as its measure in degrees.

Since segment AC is the diameter of the circle, it divides the circle into two equal parts. Hence, angle BAC is a right angle, which measures 90 degrees.

Now, we know that a circle has 360 degrees in total. We can therefore use the proportion:

90 degrees is to the measure of the arc AB as 360 degrees is to the circumference C.

Using this proportion, we can find the measure of the arc AB:

90 degrees / 360 degrees = AB / C.

Simplifying the proportion:

1/4 = AB / C.

To determine the circumference C, we can use the formula:

C = πd,

where d is the diameter. In this case, the diameter is AC, which measures 21 cm. Therefore:

C = π × 21 cm.

Using the approximate value of π as 3.14:

C ≈ 3.14 × 21 cm.

Calculating C:

C ≈ 65.94 cm.

Now, plugging this value back into the proportion:

1/4 = AB / 65.94 cm.

To find the value of AB, we can rearrange the equation:

AB = 1/4 × 65.94 cm.

Simplifying the expression:

AB ≈ 16.48 cm.

Therefore, the length of arc AB is approximately 16.48 cm.