For the assertion concerning the refinement , it suffices to show that the result will hold if we add one extra point to the partition . F is on the line segment between D and B . C is on the line segment between E and F . The line determined by OC intersects the line determined by AB at a point G which is on the line segment between A and B . E is on the line segment between A and H .
E is on the line segment between A and D .
F is on the line segment between D and B . C is on the line segment between E and F .