MathDB

6

Part of 1972 Czech and Slovak Olympiad III A

Problems(1)

Construction of points

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

7/10/2024
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).
geometrygeometric transformationrotationconstructiongeometric construction