Proper intersections
Source: 42nd International Tournament of Towns, Junior A-Level P1, Fall 2020
February 18, 2023
geometryTournament of Towns
Problem Statement
Let us say that a circle intersects a quadrilateral properly if it intersects each of the quadrilateral’s sides at two distinct interior points. Is it true that for each convex quadrilateral there exists a circle which intersects it properly?Alexandr Perepechko