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Compute the volume of EFGE'F'G', starting with a regular tetrahedron

Source: Vietnamese MO (VMO) 1972

August 24, 2018

geometrytetrahedronangles3-Dimensional Geometrysolid geometry3D geometry

Problem Statement

Let

ABCD

be a regular tetrahedron with side

a

. Take

E,E'

on the edge

AB, F, F'

on the edge

AC

and

G,G'

on the edge AD so that

AE =a/6,AE' = 5a/6,AF= a/4,AF'= 3a/4,AG = a/3,AG'= 2a/3

. Compute the volume of

EFGE'F'G'

in term of

a

and find the angles between the lines

AB,AC,AD

and the plane

EFG