IMO Shortlist 1960 problem 5
Consider the cube
(with face
directly above face
).
a) Find the locus of the midpoints of the segments
, where
is any point of
and
is any piont of
;
b) Find the locus of points
which lie on the segment
of part a) with
.
%V0
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 piont of $B'D'$;
b) Find the locus of points $Z$ which lie on the segment $XY$ of part a) with $ZY=2XZ$.
Source: Međunarodna matematička olimpijada, shortlist 1960
Školjka 
