2001 AIME I Problems/Problem 13
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
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We let our chord of degree be
, of degree
be
, and of degree
be
. We are given that
. 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 • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |