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MathNet 2010 — Part 05 Question 93

Math Olympiad Vault · MathNet 2010 — Part 05

Question 93

The Base of a Pyramid $SABCD$ is a parallelogram $ABCD$. Prove that for each point inside $SABCD$, The Sum of Volumes of Tetrahedra $OSAB$ and $OSCD$ Equal to the sum of volumes of tetrahedra $OSBC$ and $OSDA$. At the base of the quadrangular pyramid $SABCD$ lies a parallelogram $ABCD$. Prove that for any point $O$ Inside the pyramid sum of the volumes of tetrahedrons $OSAB$ and $OSCD$ equal to the sum of the volumes of tetrahedrons $OSBC$ and $OSDA$.