ASU 152 All Soviet Union MO 19 equal perimeter + equal areas through incenter
Source:
July 3, 2019
geometryperimeterareasincenter
Problem Statement
a) Prove that the line dividing the triangle onto two polygons with equal perimeters and equal areas passes through the centre of the inscribed circle. b) Prove the same statement for the arbitrary tangential polygon. c) Prove that all the lines halving its perimeter and area simultaneously, intersect in one point.