gmatt1476 wrote:
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. \(\sqrt{3}\)
PS57402.01
Attachment:
2019-09-21_1817.png
GIVEN: The length of PQ is 2
In other words, the DIAMETER = 2
From this, we can conclude that the RADIUS =
1So, we can add this information to our diagram:
Since ΔRST is equilateral, we know the altitude (TO) will be a
perpendicular bisector of side RS
Also, since ΔRST is equilateral, we know that ∠ORT = 60°, which also means ∠RTO = 30°
At this point, we can see that
ΔTRO is a special 30-60-90 triangle.
If we compare
ΔTRO with the
BASE 30-60-90 triangle, we can create an equation by comparing
corresponding sidesWe can write:
x/
2 =
1/
(√3)Multiply both sides by 2 to get: x = 2/(√3)
Answer: D
What is the use of data given PR= SQ in this question? Is it to confirm that Line from T to O will be median thus perpendicular bisector in equilateral triangle