Tetrahedron with similar right-triangle faces
Source: Czech and Slovak Olympiad 1970, National Round, Problem 2
July 4, 2024
geometry3D geometrytetrahedronright triangleright anglesimilarsimilar triangles
Problem Statement
Determine whether there is a tetrahedron with the longest edge of length 1 such that all its faces are similar right triangles with right angles at vertices If so, determine which edge is the longest, which is the shortest and what is its length.