1961 IMO Problems/Problem 6
Problem
Consider a plane and three non-collinear points
on the same side of
; suppose the plane determined by these three points is not parallel to
. In plane
take three arbitrary points
. Let
be the midpoints of segments
; Let
be the centroid of the triangle
. (We will not consider positions of the points
such that the points
do not form a triangle.) What is the locus of point
as
range independently over the plane
?
Solution
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