The Geometry Involving a Right-Cevian Triangle

This paper presents some significant theorems and corollaries prevailed, involving the cevian triangles, in particular, on right cevian triangles. Some useful corollaries are presented including a main theorem on right cevian triangles with detailed proofs, involving the ratios generated by the end points of internal cevians drawn to the side lengths of a triangle, adducing more generalized formulas for the different cevians of triangles around the right cevian triangle to fulfil the existing significant research gap in cevian geometry, particularly 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. Keywords: Cevian; Cevian Triangles; Mathematical Logic; Inequalities; Cubic Equations