- In geometry, an
orthocentric system is a set of four
points on a plane, one of
which is the
orthocenter of the
triangle formed by the
other three. Equivalently...
-
formed by the
other three, is
called an
orthocentric system or
orthocentric quadrangle. In geometry, an
orthocentric system is a set of four
points on a plane...
- In geometry, an
orthocentric tetrahedron is a
tetrahedron where all
three pairs of
opposite edges are perpendicular. It is also
known as an orthogonal...
-
rhombohedron necessarily form the four
vertices of an
orthocentric tetrahedron, and all
orthocentric tetrahedra can be
formed in this way. The rhombohedral...
-
incircle and
excircles of a
triangle form an
orthocentric system. The nine-point
circle created for that
orthocentric system is the cir****circle of the original...
- of the
other two. The
centers of the
incircles and
excircles form an
orthocentric system. The
midpoints of the
three sides and the feet of the
three altitudes...
-
center of the
incircle together with the
three excircle centers form an
orthocentric system.
Suppose △ A B C {\displaystyle \triangle ABC} has an incircle...
- has been done for
orthocentric tetrahedra (i.e.,
tetrahedra in
which altitudes are concurrent) and more
generally for
orthocentric simplices (i.e., simplices...
- then it is
called an
orthocentric tetrahedron. When only one pair of
opposite edges are perpendicular, it is
called a semi-
orthocentric tetrahedron. In a...
- follows: Let A, B, C, D be four
points in the
plane that do not form an
orthocentric system and such that no
three of them are collinear. The nine-point circles...
