(setq A (point 3 3))
(setq B (point 5 8))
(setq C (point 7 3))
(setq triangle_a (triangle A B C))
(setq O (centroid triangle_a))
(setq line_A (lineseg A O))
(setq line_B (lineseg B O))
(setq line_C (lineseg C O))

triangle_a
O
line_A
line_B
line_C
(intersect line_A (lineseg B C))
(intersect line_B (lineseg A C))
(intersect line_C (lineseg A B))