MathNet 2015-part-04 — 191 problems (EN–VI) Question 168

Let $ABCDA'B'C'D'$ be a cuboid and $AB' \cap A'B = \{O\}$. Let $N$ be a point on the edge $[BC]$ so that $A'C \parallel (B'AN)$. It is known that $D'O \perp (B'AN)$. Prove that $ABCDA'B'C'D'$ is a cube.

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