Difference between revisions of "1995 OIM Problems/Problem 3"
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− | Let <math>r</math> and <math>s</math> be two orthogonal lines that are not in the same plane. Let <math>AB</math> be their common perpendicular, | + | Let <math>r</math> and <math>s</math> be two orthogonal lines that are not in the same plane. Let <math>AB</math> be their common perpendicular, where <math>A \in r</math>, and <math>B \in s</math> '''(*)'''. |
The sphere of diameter <math>AB</math> is considered. The points <math>M</math> of the line <math>r</math>, and <math>N</math> of the line <math>s</math>, are variables, with the condition that <math>MN</math> is tangent to the sphere at a point <math>T</math>. | The sphere of diameter <math>AB</math> is considered. The points <math>M</math> of the line <math>r</math>, and <math>N</math> of the line <math>s</math>, are variables, with the condition that <math>MN</math> is tangent to the sphere at a point <math>T</math>. |
Latest revision as of 14:48, 13 December 2023
Problem
Let and
be two orthogonal lines that are not in the same plane. Let
be their common perpendicular, where
, and
(*).
The sphere of diameter is considered. The points
of the line
, and
of the line
, are variables, with the condition that
is tangent to the sphere at a point
.
Find the locus of T.
Note (*): the plane containing and
is perpendicular to
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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