棱切球四面体各侧面内心连线的几何不等式

Geometric Inequalities of the Lines Between the Incenters in Each Side for a Edge-Tangent’s Sphere Tetrahedron

摘要: 四面体存在棱切球的充要条件是该四面体的三组对棱之和相等。对于存在棱切球的四面体，本文给出有关其各侧面内心连线与棱切球半径、该四面体体积的几何不等式。

Abstract: The sufficient and necessary condition for the tetrahedron to have a edge-tangent’s sphere is that the sum of the three groups of opposite edges is equal in the tetrahedron. For a tetrahedron with a edge-tangent’s sphere, we give some geometric inequalities about the lines between the incenters in each side, the radius of the edge-tangent’s sphere and the volume of the tetrahedron in this paper.