6

Part of 1966 Poland - Second Round

Problems(1)

sum of squares of projextions is fixed, equilateral

Source: Polish MO second round 1966 p6

Prove that the sum of the squares of the right-angled projections of the sides of a triangle onto the line

p

of the plane of this triangle does not depend on the position of the line

p

if and only if it the triangle is equilateral.

geometryfixedEquilateral