Mediterranean points
Source: MMC 2015, Problem 3
March 29, 2016
geometryalgebraMediterraneanTrianglefunctional equation
Problem Statement
In the Cartesian plane each triangle contains a Mediterranean point on its sides or in its interior, even if the triangle is degenerated into a segment or a point. The Mediterranean points have the following properties:
(i) If a triangle is symmetric with respect to a line which passes through the origin , then the Mediterranean point lies on this line.
(ii) If the triangle contains the triangle and if the triangle contains the Mediterranean points of then is the Mediterranean point of the triangle Find all possible positions for the Mediterranean point of the triangle with vertices