MathDB

2

Part of 1972 Czech and Slovak Olympiad III A

Problems(1)

Locus on the surface of a cube

Source: Czech and Slovak Olympiad 1972, National Round, Problem 2

7/10/2024
Let ABCDA′B′C′D′ABCDA'B'C'D' be a cube (where ABCDABCD is a square and AA′∥BB′∥CC′∥DD′AA'\parallel BB'\parallel CC'\parallel DD'). Furthermore, let R\mathcal R be a rotation (with respect some line) that maps vertex AA to B.B. Find the set of all images X=R(C)X=\mathcal R(C) such that XX lies on the surface of the cube for some rotation R(A)=B.\mathcal R(A)=B.
geometry3D geometrygeometric transformationrotationLocus