24

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

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

Source: Sharygin 2005 X-XI CR 24

A triangle is given, all the angles of which are smaller than

\phi

\phi <2\pi / 3

. Prove that in space there is a point from which all sides of the triangle are visible at an angle

\phi

combinatorial geometrygeometryangles3D geometry