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collinearities by 2 squares (2023 Novosibirsk Oral Geo Oly 7.7)

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September 4, 2023
geometrycollegeSquares

Problem Statement

Squares ABCDABCD and BEFGBEFG are located as shown in the figure. It turned out that points A,GA, G and EE lie on the same straight line. Prove that then the points D,FD, F and EE also lie on the same line. https://cdn.artofproblemsolving.com/attachments/4/2/9faf29a399d3a622c84f5d4a3cfcf5e99539c0.png
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