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 is a central angle of the circle. From the figure, the two diameters that meet to form are perpendicular, so the measure of is . Therefore, the length of minor arc is of the circumference of the circle. Since the circumference of the circle is 36, the length of minor arc is . Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc is of the circumference. However, the lengths in choices B and C are, respectively, and the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is the circumference.

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