The circle above with center O has a circumference of 36. What is the length of minor arc $A, C$ ?
A.
9

B.
12

C.
18

D.
36

Question

The circle above with center O has a circumference of 36. What is the length of minor arc ?

Accepted Answer

Choice A is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and $angle A, O C$ is a central angle of the circle. From the figure, the two diameters that meet to form $angle A, O C$ are perpendicular, so the measure of $angle A, O C$ is $90 degrees$ . Therefore, the length of minor arc $A, C$ is $the fraction 90 over 360$ of the circumference of the circle. Since the circumference of the circle is 36, the length of minor arc $A, C$ is $the fraction 90 over 360, end fraction, times 36, equals 9$ .

Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc $A, C$ is $one fourth$ of the circumference. However, the lengths in choices B and C are, respectively, $one third$ and $one half$ the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is $one fourth$ the circumference.

Question the-ci

The circle above with center O has a circumference of 36. What is the length of

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