Given 5 coplanar points with no three collinear, prove that there must be a subset of 4 points that form a convex quadrilateral.

(In reply to another proof by Charlie)

In response to Jer's comment, replace my last paragraph with:

If the two outer points are within the same vertical angle, then the line connecting these two points will separate the triangle into two parts, with two points on one side and one point on the other, or not intersect the triangle at all.  In the former case, the two points that are on one side, together with the two outer points, then form a convex quadrilateral. In the latter case, the two points that are in the vertical angle together with any two of the vertices of the triangle will form a convex quadrilateral.

 

Posted by Charlie on 2009-10-07 12:06:19