MathDB

30

-gon

A_1A_2\cdots A_{30}

is inscribed in a circle of radius

2

. Prove that one can choose a point

B_k

on the arc

A_kA_{k+1}

for

1 \leq k \leq 29

and a point

B_{30}

on the arc

A_{30}A_1

, such that the numerical value of the area of the

60

-gon

A_1B_1A_2B_2 \dots A_{30}B_{30}

is equal to the numerical value of the perimeter of the original

30

-gon.

Problem Statement