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India National Olympiad
1992 India National Olympiad
9
What is n???
What is n???
Source: INMO 1992 Problem 9
October 4, 2005
calculus
geometry
circumcircle
trigonometry
perpendicular bisector
trig identities
Law of Sines
Problem Statement
Let
A
1
,
A
2
,
…
,
A
n
A_1, A_2, \ldots, A_n
A
1
,
A
2
,
…
,
A
n
be an
n
n
n
-sided regular polygon. If
1
A
1
A
2
=
1
A
1
A
3
+
1
A
1
A
4
\frac{1}{A_1 A_2} = \frac{1}{A_1 A_3} + \frac{1}{A_1A_4}
A
1
A
2
1
=
A
1
A
3
1
+
A
1
A
4
1
, find
n
n
n
.
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