题目信息
In the figure above, PQ is a diameter of circle O, PR = SQ, and ΔRST is equilateral. If the length of PQ is 2, what is the length of RT ?
A:
B:
C:
D:
E:
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已选答案：
正确答案：
D:
Geometry Triangles
Since PR = SQ, it follows that RO = OS, so O is the midpoint of
. Since ΔRST is equilateral and O is the midpoint of 
, ΔROT is a 30°–60°–90° triangle, and since 
is a radius of the circle with diameter 2, OT = 1. Using the ratios of the sides of a 30°–60°–90° triangle, it follows that RT = 
.
The correct answer is D.
Since PR = SQ, it follows that RO = OS, so O is the midpoint of
. Since ΔRST is equilateral and O is the midpoint of , ΔROT is a 30°–60°–90° triangle, and since is a radius of the circle with diameter 2, OT = 1. Using the ratios of the sides of a 30°–60°–90° triangle, it follows that RT = .The correct answer is D.
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