Category: Objects defined for a triangle

Pedal triangle
In geometry, a pedal triangle is obtained by projecting a point onto the sides of a triangle. More specifically, consider a triangle ABC, and a point P that is not one of the vertices A, B, C. Drop pe
Median triangle
The median triangle of a given (reference) triangle is a triangle, the sides of which are equal and parallel to the medians of its reference triangle. The area of the median triangle is of the area of
Medial triangle
The medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC and BC. It is the n=3 case of the midpoint polygon of a polygon
Tangential triangle
In geometry, the tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at the referenc
Fuhrmann triangle
The Fuhrmann triangle, named after Wilhelm Fuhrmann (1833–1904), is special triangle based on a given arbitrary triangle. For a given triangle and its circumcircle the midpoints of the arcs over trian
One-seventh area triangle
In plane geometry, a triangle ABC contains a triangle having one-seventh of the area of ABC, which is formed as follows: the sides of this triangle lie on cevians p, q, r where p connects A to a point
Extouch triangle
In geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle.