IMO 1982 LL BEL6

On the three distinct lines a, b, and c three points A, B, and

IMO 1982 LL BEL6

Origin: BEL

Problem

On the three distinct lines a, b, and c three points A, B, and C are given, respectively. Construct three collinear points X, Y, Z on lines a, b, c, respectively, such that BY AX = 2 and CZ AX = 3.