In Euclidean geometry, the exsymmedians are three lines associated with a triangle. More precisely, for a given triangle the exsymmedians are the tangent lines on the triangle's circumcircle through the three vertices of the triangle. The triangle formed by the three exsymmedians is the tangential triangle; its vertices, that is the three intersections of the exsymmedians, are called exsymmedian points.
For a triangle with being the exsymmedians and being the symmedians through the vertices , two exsymmedians and one symmedian intersect in a common point:
The length of the perpendicular line segment connecting a triangle side with its associated exsymmedian point is proportional to that triangle side. Specifically the following formulas apply:
Here denotes the area of the triangle , and denote the perpendicular line segments connecting the triangle sides with the exsymmedian points .