1960 IMO Problems/Problem 5

Problem

Consider the cube $ABCDA'B'C'D'$ (with face $ABCD$ directly above face $A'B'C'D'$ ).

a) Find the locus of the midpoints of the segments $XY$ , where $X$ is any point of $AC$ and $Y$ is any point of $B'D'$ ;

b) Find the locus of points $Z$ which lie on the segment $XY$ of part a) with $ZY = 2XZ$ .

This problem needs a solution. If you have a solution for it, please help us out by adding it.

1960 IMO (Problems) • Resources
Preceded by Problem 4	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 6
All IMO Problems and Solutions