Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

In the figure above, O is the center of the circle and  is equilateral. If the sides of are of length 6, what is the length of ?

(A)  

(B)  

(C)  

(D)  9

(E)  12

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The correct answer is C

Explanation

Choice (C) is correct. Since △ABO is equilateral, each of its angles has measure 60°. It follows that ∠BOC has measure 120°. Since  and  are radii of the same circle, they are of equal length, and so △OCB is isosceles. Hence ∠OBC and ∠OCB each have measure 30°. Thus ∠ABC has measure 60° + 30° = 90°, and so △ABC is a 30°-60°-90° right triangle. Since , the side opposite the 30° angle in △ABC, is of length 6, it follows that , the side opposite the 60° angle, is of length .