Problem 6

Part of 1990 Bulgaria National Olympiad

Problems(1)

tetrahedron, RS≥2V, S=area of base

Source: Bulgaria 1990 P6

ABC

of a tetrahedron

MABC

is an equilateral triangle, and the lateral edges

MA,MB,MC

are sides of a triangle of the area

S

R

is the circumradius and

V

the volume of the tetrahedron, prove that

RS\ge2V

. When does equality hold?

geometry3D geometrytetrahedronGeometric Inequalitiesinequalities