For triangle ABC and an arbitrary point P,[br]- Triangle DEF is the [b]medial[/b] triangle (all vertices are midpoints of the original triangle sides)[br]- Triangle GHI is the [b]orthic[/b] triangle (all vertices are feet of attitudes of original triangle vertices to the opposite sidelines)[br]- Triangle RST is the [b]cevian[/b] triangle of point P (all vertices are the intersection points of the lines joining point P and the original triangle vertices to the opposite sidelines)[br]- Triangle P[sub]A[/sub]P[sub]B[/sub]P[sub]C[/sub] is the [b]pedal[/b] triangle of point P (all vertices are the feet of attitudes of point P to the original triangle sidelines)[br]Try to drag point P (even outside the triangle ABC) or triangle vertices (even crossing the opposite side) to see the changes of four triangles.