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 13:48, 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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