TOT 248 1990 Spring A J2 intersection of 2 equal squares, ratio, equal areas
Source:
March 12, 2021
ratioSquaresequal areasgeometry
Problem Statement
If a square is intersected by another square equal to it but rotated by around its centre, each side is divided into three parts in a certain ratio (which one can compute). Make the following construction for an arbitrary convex quadrilateral: divide each of its sides into three parts in this same ratio , and draw a line through the two division points neighbouring each vertex. Prove that the new quadrilateral bounded by the four drawn lines has the same area as the original one. (A. Savin, Moscow)