Problem

Source: Iran 3rd round 2014-Algebra exam-P1

Tags: geometry, circumcircle, geometry proposed



We have an equilateral triangle with circumradius $1$. We extend its sides. Determine the point $P$ inside the triangle such that the total lengths of the sides (extended), which lies inside the circle with center $P$ and radius $1$, is maximum. (The total distance of the point P from the sides of an equilateral triangle is fixed ) Proposed by Erfan Salavati