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IX.12

Part of Ukrainian TYM Qualifying - geometry

Problems(1)

area of section of cube by plane equal to area of section of tetrahedron ...

Source: IX All-Ukrainian Tournament of Young Mathematicians, Qualifying p12

5/26/2021
Let AB,ACAB,AC and ADAD be the edges of a cube, AB=αAB=\alpha. Point EE was marked on the ray ACAC so that AE=λαAE=\lambda \alpha, and point FF was marked on the ray ADAD so that AF=μαAF=\mu \alpha (μ>0,λ>0\mu> 0, \lambda >0). Find (characterize) pairs of numbers λ\lambda and μ\mu such that the cross-sectional area of ​​a cube by any plane parallel to the plane BCDBCD is equal to the cross-sectional area of ​​the tetrahedron ABEFABEF by the same plane.
geometry3D geometrytetrahedronUkrainian TYM