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Mathematics > Standard Multiple Choice

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In the figure above, inscribed triangle A B C is equilateral. If the radius of the circle is r, then the length of arc A X B is

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An equilateral triangle has three equal sides, so the lengths of the three arcs must be equal, and thus each arc is 1 over 3 of the circumference of the circle. The circumference of the circle is 2 times pi times r, so the length of arc A X B is 1 over 3 of 2 times pi times r, or (2 times pi times r) over 3.

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