Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
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
(A) (2 times pi times r) over 3
(B) (4 times pi times r) over 3
(C) (3 times pi times r) over 2
(D) (pi times r^2) over 3
(E) (2 times pi times r^2) over 3
The correct answer is A
Explanation
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.