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Construction of points

Source: Czech and Slovak Olympiad 1972, National Round, Problem 6

July 10, 2024
geometrygeometric transformationrotationconstructiongeometric construction

Problem Statement

Two different points A,SA,S are given in the plane. Furthermore, positive numbers d,ωd,\omega are given, ω<180∘.\omega<180^\circ. Let XX be a point and X′X' its image under the rotation by the angle ω\omega (in counter-clockwise direction) with respect to the origin S.S. Construct all points XX such that XX′=dXX'=d and AA is a point of the segment XX′.XX'. Discuss conditions of solvability (in terms of d,ω,SAd,\omega,SA).
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