MathDB

Two equally oriented regular

2n

-gons

A_1A_2\ldots A_{2n}

and

B_1B_2\ldots B_{2n}

are given. The perpendicular bisectors

\ell_i

of the segments

A_iB_i

are drawn. Let the lines

\ell_i

and

\ell_{i+1}

intersect at the point

K_i

(hereafter we reduce indices modulo

2n

). Denote by

m_i

the line

K_iK_{i+n}

. Prove that

n{}

lines

m_i

intersect at one point and at that the angles between the lines

m_i

and

m_{i+1}

are equal.
Proposed by Chan Quang Hung (Vietnam)

Problem Statement