Equilateral triangles and squares
Source: IGO 2022 Elementary P5
December 14, 2022
iranian geometry olympiadgeometryEquilateral Trianglesquare
Problem Statement
a) Do there exist four equilateral triangles in the plane such that each two have
exactly one vertex in common, and every point in the plane lies on the boundary of at most two
of them?
b) Do there exist four squares in the plane such that each two have exactly one vertex in common, and every point in the plane lies on the boundary of at most two of them?
(Note that in both parts, there is no assumption on the intersection of interior of polygons.)Proposed by Hesam Rajabzadeh