Baltic Way 1990 · Problem 10

Geometry

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?

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Topics

Constructions, loci, concurrency and collinearity · Transformations

Solutions

Solution

Solution: The point $A$ can move any distance from its initial position - see Figure 4 and note that we can make the height $h$ arbitrarily small.

Diagram for the mathnet 00w3 1 of bw-1990-10. Figure 4

Elsewhere

AoPS · Baltic Way 1990