MathDB

29

Part of 1974 IMO Longlists

Problems(1)

Prove that A, B, C, D lie on the same line [ILL 1974]

Source:

1/2/2011
Let A,B,C,DA,B,C,D be points in space. If for every point MM on the segment ABAB the sum SAMC+SCMD+SDMBS_{AMC}+S_{CMD}+S_{DMB} Is constant show that the points A,B,C,DA,B,C,D lie in the same plane.
[hide="Note."] Note. SXS_X denotes the area of triangle X.X.
geometry