Orthologic triangles
In geometry, two triangles are said to be orthologic if the perpendiculars from the vertices of one of them to the corresponding sides of the other are concurrent. This is a symmetric property; that is, if the perpendiculars from the vertices of triangle to the sides of triangle are concurrent then the perpendiculars from the vertices of to the sides of are also concurrent. The points of concurrence are known as the orthology centres of the two triangles.
Some pairs of orthologic triangles
The following are some triangles associated with the reference triangle ABC and orthologic with it.- Medial triangle
- Anticomplementary triangle
- The triangle whose vertices are the points of contact of the incircle with the sides of ABC
- Tangential triangle
- Extouch triangle
- The triangle formed by the bisectors of the external angles of triangle ABC
- The pedal triangle of any point P in the plane of triangle ABC