- In geometry, the
incenter of a
triangle is a
triangle center, a
point defined for any
triangle in a way that is
independent of the triangle's placement...
- The
center of the
incircle is a
triangle center called the triangle's
incenter. An
excircle or
escribed circle of the
triangle is a
circle lying outside...
- In geometry, the
incenter–excenter
lemma is the
theorem that the line
segment between the
incenter and any
excenter of a triangle, or
between two excenters...
-
incircle of the
quadrilateral or its
inscribed circle, its
center is the
incenter and its
radius is
called the inradius.
Since these quadrilaterals can be...
- and
centers of
these circles are
called inradius and cir****radius, and
incenter and cir****center respectively. From the
definition it
follows that bicentric...
-
triangles formed from the four
orthocentric points taken three at a time. The
incenter of this
common orthic triangle must be one of the
original four orthocentric...
- triangle's
incenter (the
center of its incircle).
There are
either one, two, or
three of
these for any
given triangle. A line
through the
incenter bisects...
-
angle in half. The
three angle bisectors intersect in a
single point, the
incenter,
which is the
center of the triangle's incircle. The
incircle is the circle...
- it
follows that the
Euler line
coincides with the axis of symmetry. The
incenter of the
triangle also lies on the
Euler line,
something that is not true...
- not go
through its
incenter unless the
triangle is isosceles.: p.231 For all non-isosceles triangles, the
distance d from the
incenter to the
Euler line...
