A k-point if it is observable from the exactly k sides
Source: First Zhautykov Olympiad 2005, Problem 5
December 22, 2008
geometry unsolvedgeometry
Problem Statement
The inner point of a quadrilateral is observable from the side if the perpendicular to the line meet it in the colosed interval The inner point of a quadrilateral is a k\minus{}point if it is observable from the exactly sides of the quadrilateral. Prove that if a convex quadrilateral has a 1-point then it has a k\minus{}point for each k\equal{}2,3,4.