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We estabish some geometric inequalities on the inradius and circumradius of two n -dimensional simplexes. n are regular. In this paper, we establish other inequalities involving two simplexes, and give some their applications. Our main results are the following theorems. Mathematics subject classification (2000): 52A40.doi:10.7153/mia-06-14 fatcat:ujopqrd4urga3bfgfwbso3yicu