The Geometry Involving a Right-Cevian Triangle

Abstract

This paper presents some signifi cant theorems and corollaries prevailed, involving the cevian triangles, in parti cular, on right cevian triangles. Some useful corollaries are presented including a main theorem on right cevian triangles with detailed proofs, involving the rati os generated by the end points of internal cevians drawn to the side lengths of a triangle, adducing more generalized formulas for the diff erent cevians of triangles around the right cevian triangle to fulfi l the existi ng signifi cant research gap in cevian geometry, parti cularly on cevian triangles. This paper presents pure geometric proofs for the theorems and corollaries, without using trigonometry, coordinate geometry, complex numbers, vectors or any other non-geometric approaches.