MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Stanford Mathematics Tournament
2021 Stanford Mathematics Tournament
7
7
Part of
2021 Stanford Mathematics Tournament
Problems
(1)
SMT 2021 Geometry #7
Source:
8/9/2023
An
n
n
n
-sided regular polygon with side length
1
1
1
is rotated by
18
0
o
n
\frac{180^o}{n}
n
18
0
o
about its center. The intersection points of the original polygon and the rotated polygon are the vertices of a
2
n
2n
2
n
-sided regular polygon with side length
1
−
t
a
n
2
1
0
o
2
\frac{1-tan^2 10^o}{2}
2
1
−
t
a
n
2
1
0
o
. What is the value of
n
n
n
?
geometry