MathDB

4

Part of 1972 Vietnam National Olympiad

Problems(1)

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

Source: Vietnamese MO (VMO) 1972

8/24/2018
Let ABCDABCD be a regular tetrahedron with side aa. Take E,E′E,E' on the edge AB,F,F′AB, F, F' on the edge ACAC and G,G′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/3AE =a/6,AE' = 5a/6,AF= a/4,AF'= 3a/4,AG = a/3,AG'= 2a/3. Compute the volume of EFGE′F′G′EFGE'F'G' in term of aa and find the angles between the lines AB,AC,ADAB,AC,AD and the plane EFGEFG.
geometrytetrahedronangles3-Dimensional Geometrysolid geometry3D geometry