MathDB

3

Part of 1976 Vietnam National Olympiad

Problems(1)

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

Source: Vietnamese MO (VMO) 1976 P3

8/20/2018
PP is a point inside the triangle ABCABC. The perpendicular distances from PP to the three sides have product pp. Show that p≤8S327abcp \le \frac{ 8 S^3}{27abc}, where S=S = area ABCABC and a,b,ca, b, c are the sides. Prove a similar result for a tetrahedron.
geometrygeometric inequalitytetrahedronarea of a triangledistance