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SMO 2022 Open Round 1 Question 7

SMO · SMO 2022 Open Round 1

Question 7

A tetrahedron in $\mathbb R^3$ has one vertex at the origin $O$ and the other vertices at the points $A(6,0,0)$, $B(4,2,4)$ and $C(3,2,6)$. If $x$ is the height of the tetrahedron from $O$ to the plane $ABC$, find $\lfloor5x^2\rfloor$.