A Geometric Way to Generate Blundon Type Inequalities

2012/05/05 by Dorin Andrica, Andrica, Dorin, Catalin Barbu +3
Mathematics · #26D05 #26D15 #51N35 #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:26D05 #msc:26D15 #msc:51N35

paper · pdf · doi:10.48550/arxiv.1205.1145

13 pages submitted to MIA 2012

arxiv created 2012/05/05 · arxiv updated 2012/05/08

Abstract

We present a geometric way to generate Blundon type inequalities. Theorem 3.1 gives the formula for cosPOQ in terms of the barycentric coordinates of the points P and Q with respect to a given triangle. This formula implies Blundon type inequalities generated by the points P and Q (Theorem 3.2). Some applications are given in the last section by choosing special points P and Q.

Related

• A Metric Framework for Triangle Inequalities via Barycentric Coordinates
• Some extensions of a geometric inequality generated from Ptolemy’s inequality
• Ceva's triangle inequalities
• Functional inequalities derived from the Brunn-Minkowski inequalities for quermassintegrals
• Barrow's Inequality and Signed Angle Bisectors