Perpendicular bisectors of two pieces of its medians form a hexagon with opposite sides parallel. |
The common perpendicular bisectors of parallel sides bisect the angles of the triangle formed by the extensions of the three equal diagonals. |
Located where the bisectors of a triangle's three angles intersect, the incenter is the center of the largest circle that can be inscribed inside that triangle. |
It then follows from the Menelaus theorem, that every three such points are collinear provided all or two of the bisectors are external. |
Indeed, let L P, L Q and L R be the points of intersection of bisectors of angles CPB, AQC, and BRA with sides CB, AC and BA, respectively. |
The right-hand example shows the menu displayed when you point the cursor at the point of intersection between the three bisectors of a triangle. |