每日一题

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 A B O is equilateral. If the sides of triangle A B O are of length 6, what is the length of line B C?

(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 degrees. It follows that angle B O C has measure 120 degrees. 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 degrees. Thus angle A B C has measure 60 degrees + 30 degrees = 90 degrees, 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 degrees angle in triangle A B C, is of length 6, it follows that line B C, the side opposite the 60 degrees angle, is of length 6 times square root 3.