- 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...
- 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...
- 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...
-
bicentric quadrilateral and O the
center of its cir****circle. Then the
incenters of the four
triangles △OAB, △OBC, △OCD, △ODA lie on a circle. Wikimedia...
- diagonals, then the
incenters of the four
triangles are
concyclic if and only if the
quadrilateral is tangential. In fact, the
incenters form an orthodiagonal...
- 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...
- 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...
-
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...
- (dotted) and
symmedians (red). The
symmedians intersect in the
symmedian point L, the
angle bisectors in the
incenter I and the
medians in the
centroid G....
-
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...
