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4 lines in spaces, find position of a line that minimises a distance of 2 lines

Source: Vietnamese MO (VMO) 1976 P5

August 20, 2018
geometry3D geometry3-Dimensional Geometrylinesdistance

Problem Statement

L,L′L, L' are two skew lines in space and pp is a plane not containing either line. MM is a variable line parallel to pp which meets LL at XX and L′L' at YY. Find the position of MM which minimises the distance XYXY. L′′L'' is another fixed line. Find the line MM which is also perpendicular to L′′L'' .
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