1995 OIM Problems/Problem 3

Problem

Let $r$ and $s$ be two orthogonal lines that are not in the same plane. Let $AB$ be their common perpendicular, where $A \in r$, and $B \in s$ (*).

The sphere of diameter $AB$ is considered. The points $M$ of the line $r$, and $N$ of the line $s$, are variables, with the condition that $MN$ is tangent to the sphere at a point $T$.

Find the locus of T.

Note (*): the plane containing $B$ and $r$ is perpendicular to $s$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe10.htm