MMO 135 Moscow MO 1947 4 out of 5 create a convex quadrilateral
Source:
July 20, 2019
combinatorial geometrycombinatoricsgeometryconvex
Problem Statement
a) Given points on a plane, no three of which lie on one line. Prove that four of these points can be taken as vertices of a convex quadrilateral.b) Inside a square, consider a convex quadrilateral and inside the quadrilateral, take a point . It so happens that no three of the points — the vertices of the square, of the quadrilateral and — lie on one line. Prove that of these points are vertices of a convex pentagon.