Interior points of the sides minimizing the perimeter iff cyclic
Source: Germany 2021, Problem 2
June 16, 2021
geometryperimetergeometry proposedcyclic quadrilateralinterior
Problem Statement
Let on , on , on and on be points on the sides of a convex quadrilateral . Show that the following are equivalent:(1) There is a choice of , for which all of them are interior points of their side, such that has minimal perimeter.(2) is a cyclic quadrilateral with circumcenter in its interior.