SQUARE AND EQUILATERAL TRIANGLES

A Corollary of SQUARE PROBLEM

Let ABCD be a square, E,E' two points on BC such that DEE' is an equilateral triangle and I,I' the midpoints of BE,BE', resp. Denote:

F := AE /\ DC, F' := AE' /\ DC

M := IF /\ DE, M' := I'F' /\ D'E'

K := IF /\ I'F'

N := AD /\ IF, N' := AD /\ I'F'

The triangles IEM, I'E'M', KII', DMN, DM'N', KNN' are equilateral.

Antreas