sum of squares of projextions is fixed, equilateral
Source: Polish MO second round 1966 p6
August 28, 2024
geometryfixedEquilateral
Problem Statement
Prove that the sum of the squares of the right-angled projections of the sides of a triangle onto the line of the plane of this triangle does not depend on the position of the line if and only if it the triangle is equilateral.