Equilateral triangle and a point in it ( Iran 2014)
Source: Iran 3rd round 2014-Algebra exam-P1
September 19, 2014
geometrycircumcirclegeometry proposed
Problem Statement
We have an equilateral triangle with circumradius . We extend its sides. Determine the point inside the triangle such that the total lengths of the sides (extended), which lies inside the circle with center and radius , is maximum.
(The total distance of the point P from the sides of an equilateral triangle is fixed )Proposed by Erfan Salavati