IMO 1976 LL BUL5

Let ABCDS be a pyramid with four faces and with ABCD

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IMO 1976 LL BUL5

Origin: BUL

Problem

Let ABCDS be a pyramid with four faces and with ABCD as a base, and let a plane \alpha through the vertex A meet its edges SB and SD at points M and N, respectively. Prove that if the intersection of the plane \alpha with the pyramid ABCDS is a parallelogram, then SM \cdot SN > BM \cdot DN.