MathDB

5

Part of 1982 Canada National Olympiad

Problems(1)

The centroid of A"B"C"D" is the same as the centroid of ABCD

Source: Canada National Mathematical Olympiad 1982 - Problem 5

9/30/2011
The altitudes of a tetrahedron ABCDABCD are extended externally to points A′A', B′B', C′C', and D′D', where AA′=k/haAA' = k/h_a, BB′=k/hbBB' = k/h_b, CC′=k/hcCC' = k/h_c, and DD′=k/hdDD' = k/h_d. Here, kk is a constant and hah_a denotes the length of the altitude of ABCDABCD from vertex AA, etc. Prove that the centroid of tetrahedron A′B′C′D′A'B'C'D' coincides with the centroid of ABCDABCD.
geometry3D geometrytetrahedronvectorgeometry proposed