MathDB

2

Part of 1973 IMO Longlists

Problems(1)

Construct the plane which minimizes the volume

Source: IMO LongList 1973 - P2

6/6/2011
Let OX,OYOX, OY and OZOZ be three rays in the space, and GG a point "between these rays" (i. e. in the interior of the part of the space bordered by the angles YOZ,ZOXY OZ, ZOX and XOYXOY). Consider a plane passing through GG and meeting the rays OX,OYOX, OY and OZOZ in the points A,B,CA, B, C, respectively. There are infinitely many such planes; construct the one which minimizes the volume of the tetrahedron OABCOABC.
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