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MathNet 2020 — Math Olympiad Vault — Part 05 Question 126

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 126

The diagonals of the faces of the rectangular parallelepiped $ABCD'A'B'C'D'$ satisfy the relation:
$$
CA^2 = \frac{2 \cdot B'A^2 \cdot D'A^2}{B'A^2 + D'A^2}.
$$
Prove that $AC' \le \sqrt{3} \cdot AA'$.