MathDB
in space exists a point that all sides of the triangle are visible at angle \phi

Source: Sharygin 2005 X-XI CR 24

August 20, 2019
combinatorial geometrygeometryangles3D geometry

Problem Statement

A triangle is given, all the angles of which are smaller than ϕ\phi, where ϕ<2π/3\phi <2\pi / 3. Prove that in space there is a point from which all sides of the triangle are visible at an angle ϕ\phi.