Hyperbolic
orthocenter
The orthocenter is the intersection point of the three altitudes of a
triangle.
We say altitude to the perpendicular line to a side of a triangle that
passes through the vertex that does not belong to this side.
To
construct the orthocenter of a hyperbolic
triangle is necessary
to plot the three altitudes. Which it can be done easily with the
perpendicular tool for an exterior point
applied to each side and to the
opposite vertex.
The orthocenter, as the circumcenter, does not always exist.
That is, the three altitudes will not always intersect. Anyway, if two
altitudes intersect, then the third will pass through the intersection
point.
The existence of the orthocenter can be studied from the sides length
and from the angles of the triangle. A characterization can be found in
Existence
of the orthocenter. We can say that whenever the triangle has
the three acute angles the
orthocenter will exist.
Triangles
Hyperbolic
geometry
