1964 IMO Problems/Problem 6

Revision as of 11:39, 16 July 2009 by Xpmath (talk | contribs) (Solution)


In tetrahedron $ABCD$, vertex $D$ is connected with $D_0$, the centrod of $\triangle ABC$. Lines parallel to $DD_0$ are drawn through $A,B$ and $C$. These lines intersect the planes $BCD, CAD$ and $ABD$ in points $A_1, B_1,$ and $C_1$, respectively. Prove that the volume of $ABCD$ is one third the volume of $A_1B_1C_1D_0$. Is the result true if point $D_o$ is selected anywhere within $\triangle ABC$


This problem needs a solution. If you have a solution for it, please help us out by adding it.

Invalid username
Login to AoPS