- 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 the triangle...
- {a+b+c}{2}}.} In any triangle, any
vertex and the
point where the
opposite excircle touches the
triangle partition the triangle's
perimeter into two equal...
-
excircles; they lie
outside the
triangle and
touch one side, as well as the
extensions of the
other two. The
centers of the
incircles and
excircles form...
-
states more
generally that the nine-point
circle is
tangent to the
three excircles of the
triangle as well as its incircle. A very
short proof of this theorem...
-
circles Schoch circles Woo
circles Apollonius circle of the
excircles Brocard circle Excircle Incircle Lemoine circle Lester circle Malfatti circles Mandart...
- collinearities. Any vertex, the
tangency of the
opposite side with an
excircle, and the
Nagel point are
collinear in a line
called a
splitter of the triangle...
- {\displaystyle r^{2}+r_{a}^{2}+r_{b}^{2}+r_{c}^{2}<8R^{2},} in
terms of the
excircle radii ra , rb , and rc ,
again with the
reverse inequality holding for...
- TC be the
extouch points in
which the A-
excircle meets line BC, the B-
excircle meets line CA, and the C-
excircle meets line AB, respectively. The lines...
-
proportionality Euclidean geometry Golden ratio Gr****
numerals Incircle and
excircles of a
triangle Method of
exhaustion Parallel postulate Platonic solid Lune...
- also been
called an
exscriptible quadrilateral. The
circle is
called its
excircle, its
radius the
exradius and its
center the
excenter (E in the figure)...
