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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 triangle ABO is equilateral. If the sides of triangle ABO are of length 6, what is the length of BC?

(A) 3 times square root 3
(B) 4 times square root 3
(C) 6 times square root 3
(D) 9
(E) 12

答案和解析

答案：C

解析：

Choice (C) is correct. Since triangle A B O is equilateral, each of its angles has measure 60°. It follows that angle B O C has measure 120°. Since line O B and line O C are radii of the same circle, they are of equal length, and so triangle O C B is isosceles. Hence angle O B C and angle O C B each have measure 30°. Thus angle A B C has measure 60° + 30° = 90°, and so triangle A B C is a 30 degree - 60 degree - 90 degree right triangle. Since line A B, the side opposite the 30° angle in triangle A B C, is of length 6, it follows that line B C, the side opposite the 60° angle, is of length 6 times square root 3.