MathDB

The triangles

AB'C, CA'B

and

BC'A

are constructed on the sides of the equilateral triangle

ABC.

In the resulting hexagon

AB'CA'BC'

each of the angles

\angle A'BC',\angle C'AB'

and

\angle B'CA'

is greater than

120^\circ

and the sides satisfy the equalities

AB' = AC',BC' = BA'

and

CA' = CB'.

Prove that the segments

AB',BC'

and

CA'

can form a triangle.
David Brodsky

Problem Statement