5 points lie in a plane, no 3 collinear. Show that 4 of the points form a convex quadrilateral.
Solution
If the convex hull has 4 or 5 vertices, then we are done. If not, then two of the points, say D and E, must lie inside the triangle ABC formed by the other three. DE must intersect just two of AB, BC and CA. Suppose that it does not intersect AB. Then the four points A, B, D, E form a convex quadrilateral.
© John Scholes
jscholes@kalva.demon.co.uk
5 Feb 2002