MathDB

parallelogram, equilateral, collinear,rhombus (2018 Romanian NMO VII P3)

Source:

June 3, 2020

geometryparallelogramcollinearEquilateralrhombus

Problem Statement

On the sides

[AB]

and

[BC]

of the parallelogram

ABCD

are constructed the equilateral triangles

ABE

and

BCF,

so that the points

D

and

E

are on the same side of the line

AB

, and

F

and

D

on different sides of the line

BC

. If the points

E,D

and

F

are collinear, then prove that

ABCD

is rhombus.