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DE and DF trisect AB, equilaterals ABC and ADB

Source: Austria Beginners' Competition 2012 p4

December 26, 2021

geometrytrisectequilaterals

Problem Statement

A segment

AB

is given. We erect the equilateral triangles

ABC

and

ADB

above and below

AB

. We denote the midpoints of

AC

and

BC

by

E

and

F

respectively. Prove that the straight lines

DE

and

DF

divide the segment

AB

into three parts of equal length .

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