BALTIC-WAY 1990 Problem 10

Answer

A segment $A B$ of unit length is marked on the straight line $t$ . The segment is then moved on the plane so that it remains parallel to $t$ at all times, the traces of the points $A$ and $B$ do not intersect and finally the segment returns onto $t$ . How far can the point $A$ now be from its initial position?

Dataset text NuminaMath olympiads. Quoted with source.

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any\ distance

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