(Faculty of Humanities and Sciences, SLIIT, 2024-12-04) Amarasinghe, G.W.I.S
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.
