MathDB
3 distances form a rectangular parallelepiped, are sidelengths of triangle

Source: Vietnam MO 1978 P6

July 29, 2018
geometry3-Dimensional Geometrytriangle inequalitydistance

Problem Statement

Given a rectangular parallelepiped ABCDA′B′C′D′ABCDA'B'C'D' with the bases ABCD,A′B′C′D′ABCD, A'B'C'D', the edges AA′,BB′,CC′,DD′AA',BB', CC',DD' and AB=a,AD=b,AA′=cAB = a,AD = b,AA' = c. Show that there exists a triangle with the sides equal to the distances from A,A′,DA,A',D to the diagonal BD′BD' of the parallelepiped. Denote those distances by m1,m2,m3m_1,m_2,m_3. Find the relationship between a,b,c,m1,m2,m3a, b, c,m_1,m_2,m_3.
Back to ProblemsView on AoPS