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In the figure above, PQ is a diameter of circle O, PR = SQ,

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In the figure above, PQ is a diameter of circle O, PR = SQ,

by BTGmoderatorDC » Mon Dec 23, 2019 12:24 am
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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. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{\sqrt{3}}{2}\)

D. \(\frac{2}{\sqrt{3}}\)

E. \(\sqrt{3}\)




OA D

Source: Official Guide
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by Jay@ManhattanReview » Mon Dec 23, 2019 1:09 am
BTGmoderatorDC wrote:Image

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. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{\sqrt{3}}{2}\)

D. \(\frac{2}{\sqrt{3}}\)

E. \(\sqrt{3}\)

OA D

Source: Official Guide
Given that PQ = 2, we have radius of the circle = 2/2 = 1. Draw TO, thus TO = 1, radius. Since ∆RST is an equilateral triangle, thus, /_TRO = 60º, /_TOR = 90º and /_RTO = 30º.

Thus, ∆TRO is a 90-60-30 triangle. In a 90-60-30 triangle, the ratio of sides opposite to respective angles is 2 : √3 : 1. Given that TO the side opposite to /_90º is 1, thus, the side opposite to /_90º would be 2/√3.

The correct answer: D

Hope this helps!

-Jay
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