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2020 Princeton University Math Competition
9
9
Part of
2020 Princeton University Math Competition
Problems
(1)
2020 PUMaC Team 9
Source:
1/1/2022
Consider a regular
2020
2020
2020
-gon circumscribed into a circle of radius
1
1
1
. Given three vertices of this polygon such that they form an isosceles triangle, let
X
X
X
be the expected area of the isosceles triangle they create.
X
X
X
can be written as
1
m
tan
(
(
2
π
)
/
n
)
\frac{1}{m \tan((2\pi)/n)}
m
t
a
n
((
2
π
)
/
n
)
1
where
m
m
m
and
n
n
n
are integers. Compute
m
+
n
m + n
m
+
n
.
combinatorics