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Find the locus of points

Source: Vietnam NMO 1986 Problem 4

February 6, 2009
geometry unsolvedgeometry

Problem Statement

Let ABCD ABCD be a square of side 2a 2a. An equilateral triangle AMB AMB is constructed in the plane through AB AB perpendicular to the plane of the square. A point S S moves on AB AB such that SB\equal{}x. Let P P be the projection of M M on SC SC and E E, O O be the midpoints of AB AB and CM CM respectively. (a) Find the locus of P P as S S moves on AB AB. (b) Find the maximum and minimum lengths of SO SO.
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