Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
Let
I
n
I_n
I
n
is the area of
n
n
n
-sided regular polygon inscribed in a circle of unit radius and
O
n
O_n
O
n
be the area of the polygon circumscribing the given circle. Then, prove that
I
n
=
O
n
2
(
1
+
1
−
(
2
I
n
O
n
)
2
)
I_n = \frac{O_n}{2} \left( 1 + \sqrt{1 - \left(\frac{2I_n}{O_n}\right)^2} \right)
I
n
=
2
O
n
(
1
+
1
−
(
O
n
2
I
n
)
2
)
.
Browse the problem library