2001 AIME I Problems/Problem 13
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Problem
In a certain circle, the chord of a 
-degree arc is 
centimeters long, and the chord of a 
-degree arc is 
centimeters longer than the chord of a 
-degree arc, where 
The length of the chord of a -degree arc is 
centimeters, where 
and 
are positive integers. Find 
Solution
We let our chord of degree be 
, of degree be 
, and of degree be 
. We are given that 
. Let 
. Since 
, quadrilateral 
is a cyclic isosceles trapezoid, and so 
. By Ptolemy's Theorem, we have
Therefore, the answer is 
.
See also
| 2001 AIME I (Problems • Resources) | ||
| Preceded by Problem 12 | Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
