swerve wrote: ↑Tue Jan 21, 2020 12:42 pm
In the figure below, 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. \(\sqrt{3}\)
The OA is
D
Source: Official Guide
Join OT. Thus, OT = 1 , radius.
You would observe that ∆RTO is a rightangled triangle, with /_TOR = 90º; /_TRO = 60º (given that ∆RST is an equilateral triangle); thus, /_RTO = 30º. Thus, ∆RTO is a 30-60-90 rightangled triangle.
Note that the sides of a 30-60-90 rightangled triangle are in the ratio of 1 : √3 : 2, respectively. Thus, RT = (2/√3)*OT = (2/√3)*1 = 2/√3
The correct answer:
D
Hope this helps!
-Jay
_________________
Manhattan Review
Locations:
Manhattan Review Kukatpally |
GMAT Prep Jayanagar |
GRE Prep Tarnaka |
Madhapur GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
