In the figure above，PQ is a diameter of circle O，PR=SQ，and △RST is equilateral．If the length of PQ is 2．what is the length of RT

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问题

In the figure above，PQ is a diameter of circle O，PR=SQ，and △RST is equilateral．If the length of PQ is 2．what is the length of RT?

选项 A、
B、
C、
D、
E、

答案D

解析 Since PR = SQ it follows that RO = OS, so O is the midpoint of RS. Since △RST is equilateral and 0 is the midpoint of

, △ROT 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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