Find the length of arc AC if the diameter, AB, of circle O is 36 cm. Write answer in terms of pi.
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We do not know where C is situated on the circle, since we do not see a figure, nor descriptions. Please supply more information if an answer is desired.
To find the length of arc AC, we need to know the measure of the central angle that corresponds to this arc.
Since we are given the diameter AB, we know that AB is twice the radius of the circle. Therefore, the radius of the circle is 36 cm ÷ 2 = 18 cm.
Next, we need to find the central angle that corresponds to arc AC. The central angle is formed by the radius of the circle and the two endpoints of the arc.
Since AB is the diameter of the circle, it divides the circle into two equal parts, making angle AOB a right angle (90 degrees). Therefore, the central angle AOC is half of angle AOB.
So, the central angle AOC is 90 degrees ÷ 2 = 45 degrees.
Now we can find the length of arc AC using the formula:
Arc Length = (Central Angle/360 degrees) × Circumference of the Circle
The circumference of the circle is given by 2πr, where r is the radius. So, substituting the values, we get:
Arc Length = (45 degrees/360 degrees) × 2π × 18 cm
Arc Length = (1/8) × 2π × 18 cm
Arc Length = π × 9 cm
Arc Length = 9π cm
Therefore, the length of arc AC is 9π cm.