MathDB

Locus of vertices of equilateral triangles

Source: Czech and Slovak Olympiad 1981, National Round, Problem 3

October 11, 2024

geometryLocussquareEquilateralTriangle

Problem Statement

Let

ABCD

be a unit square. Consider an equilateral triangle

XYZ

with

X,Y

as (inner or boundary) points of the square. Determine the locus

M

of vertices

Z

of all these triangles

XYZ

and compute the area of

M.