I find this : " . . . bisect its angles ( blue ), and drop perpendiculars from the point where the bisectors meet to the three sides ( green ).
42.
This property of automedian triangles stands in contrast to the Steiner Lehmus theorem, according to which the only triangles two of whose angle bisectors have equal length are the isosceles triangles.
43.
Similar arguments show that the center mass of the three particle system lies on the internal bisectors of " " E " and " " F " also.
44.
In an obtuse triangle the two shortest sides'perpendicular bisectors ( extended beyond their opposite triangle sides to the circumcenter ) are divided by their respective intersecting triangle sides in equal proportions.
45.
These six lines are concurrent three at a time : in addition to the three medians being concurrent, any one median is concurrent with two of the side-parallel area bisectors.
46.
These inequalities deal with the lengths " p " " a " etc . of the triangle-interior portions of the perpendicular bisectors of sides of the triangle.
47.
:The dihedral group of a regular " n " sided polygon is generated by the reflections in the perpendicular bisectors of its sides and the bisectors of its interior angles.
48.
:The dihedral group of a regular " n " sided polygon is generated by the reflections in the perpendicular bisectors of its sides and the bisectors of its interior angles.
49.
As mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the perpendicular bisectors of the triangle's sides.
50.
The center of an excircle is the intersection of the internal bisector of one angle ( at vertex " A ", for example ) and the external bisectors of the other two.
