MathDB

Points

M

and

N

are the midpoints of sides

AB

and

BC

of the square

ABCD

. According to the fgure, we have drawn a regular hexagon and a regular

12

-gon. The points

P, Q

and

R

are the centers of these three polygons. Prove that

PQRS

is a cyclic quadrilateral.
Proposed by Mahdi Etesamifard - Iran

Problem Statement