MathDB

Two equal-sized regular

n

-gons intersect to form a

2n

-gon

C

. Prove that the sum of the sides of

C

which form part of one

n

-gon equals half the perimeter of

C

.
Alternative formulation:
Let two equal regular

n

-gons

S

and

T

be located in the plane such that their intersection

S\cap T

is a

2n

-gon (with

n\ge 3

). The sides of the polygon

S

are coloured in red and the sides of

T

in blue.
Prove that the sum of the lengths of the blue sides of the polygon

S\cap T

is equal to the sum of the lengths of its red sides.

3