MathDB

p<= 8S^3 / 27abc, where p is product of distances of P from sides of ABC, S=area

Source: Vietnamese MO (VMO) 1976 P3

August 20, 2018

geometrygeometric inequalitytetrahedronarea of a triangledistance

Problem Statement

P

is a point inside the triangle

ABC

. The perpendicular distances from

P

to the three sides have product

p

. Show that

p \le \frac{ 8 S^3}{27abc}

, where

S =

area

ABC

and

a, b, c

are the sides. Prove a similar result for a tetrahedron.