Difference between revisions of "1961 IMO Problems/Problem 6"
(New page: ==Problem== Consider a plane <math>\epsilon</math> and three non-collinear points <math>A,B,C</math> on the same side of <math>\epsilon</math>; suppose the plane determined by these three...) |
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Revision as of 11:36, 12 October 2007
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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