MathDB
Infinitely many rotations around a fixed axis

Source: IMO Longlist 1989, Problem 107

September 18, 2008
geometrygeometric transformationrotationgeometry unsolved

Problem Statement

Let Ax,By Ax,By be two perpendicular semi-straight lines, being not complanar, (non-coplanar rays) such that AB AB is the their common perpendicular, and let M M and N N be the two variable points on Ax Ax and Bx, Bx, respectively, such that AM \plus{} BN \equal{} MN. (a) Prove that there exist infinitely many lines being co-planar with each of the straight lines MN. MN. (b) Prove that there exist infinitely many rotations around a fixed axis δ \delta mapping the line Ax Ax onto a line coplanar with each of the lines MN. MN.
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