On a triangle inequality involving angle bisectors
Let a, b and c be the sides of a triangle and la, lb, and lc be the lengths of its angle bisectors.
We prove the following inequality:
J3 Triangular Cupola
A cupola is a polyhedron with two opposite polygons, of which one has twice as many vertices as the other and with alternating triangles and quadrangles as side faces. When all faces of the cupola are regular, then the cupola is a Johnson solid. There are three regular cupolae, the triangular (J3), the square (J4) and the pentagonal (J5) cupola. The triangular cupola has 4 equilateral triangles, 3 squares, and a regular hexagon, for a total of 8 faces, 15 edges, and 9 vertices. More information can be read here: http://eusebeia.dyndns.org/4d/J3 https://polytope.miraheze.org/wiki/Triangular_cupola You can download the Geogebra construction here: https://www.geogebra.org/m/x48ntrx4 . Sample stereometry problem: Prove that the angle 𝜃 between the planes (ABI) and (CDH) has cos(𝜃)=7/11.
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