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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
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
admin
2022-10-18
104
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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