MathDB
line bisecting area and perimeter, incenter - 1993 Cono Sur Shortlist G9

Source:

October 24, 2021
geometryperimeterbisectorareasincenter

Problem Statement

Prove that a line that divides a triangle into two polygons of equal area and equal perimeter passes through the center of the circle inscribed in the triangle. Prove an analogous property for a polygon that has an inscribed circle.