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Hexagon with a center of symmetry

Source: Poland Math Olympiad 1992 First Round #3

June 2, 2023

symmetry

Problem Statement

Given is a hexagon

ABCDEF

with a center of symmetry. The lines

AB

and

EF

meet at the point

A'

, the lines

BC

and

AF

meet at the point

B'

, and the lines

AB

and

CD

meet at the point

C'

. Prove that

AB \cdot BC \cdot CD = AA' \cdot BB' \cdot CC'

.

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