1994 AIME Problems/Problem 8
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Problem
The points 
, 
, and 
are the vertices of an equilateral triangle. Find the value of 
.
Solution
Consider the points on the complex plane. The point 
is then a rotation of 
degrees of 
about the origin, so:
Equating the real and imaginary parts, we have:
Solving this system, we find that 
. Thus, the answer is 
.
See also
| 1994 AIME (Problems • Resources) | ||
| Preceded by Problem 7 | Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
