# 1960 IMO Problem 5

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• Vinuthan S
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### 1960 IMO Problem 5

#### 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 $ZY=2XZ$.

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