Discrete Mathematics: Elementary and Beyond

11.3 Convex Polygons 187

11.3.3Into how many parts do two triangles divide the plane?

11.3.4Into how many parts do two quadrilaterals divide the plane, if

(a) they are convex,

(b) they are not necessarily convex?

11.3.5Into how many parts do two convexn-gons divide the plane?

11.3.6Into how many parts canncircles divide the plane, maximum and min-
imum?

11.3.7Prove that 6 points in the plane, no 3 on a line, form at least 3 convex
quadrilaterals.

11.3.8Given a setSof 100 points in the plane, no 3 on a line, show that there
is a convex polygon whose vertices are in the setSand that contains exactly 50
points ofS(including its vertices).