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Question: A, B, C, D is a tetrahedron, A<sub>1</sub>, B<sub>1</sub>, C<sub>1</sub>, D<sub>1</sub> are respecti...

A, B, C, D is a tetrahedron, A1, B1, C1, D1 are respectively the centroids of the triangles BCD, ACD, ABD and ABC ; AA1 , BB1, CC1, DD1 divide one another in the ratio

A

1 : 1

B

2 : 1

C

3 : 1

D

1 : 3

Answer

3 : 1

Explanation

Solution

It is clear, AA1, BB1, CC1, DD1 meet at centroid of the

tetrahedron ABCD. If centroid is G then

AGGA1\frac{AG}{GA_{1}} = BGGB1\frac{BG}{GB_{1}} = CGGC1\frac{CG}{GC_{1}} = DGGD1\frac{DG}{GD_{1}} = 31\frac{3}{1}