Straight lines defined for a triangle
Exsymmedian
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 and 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, that is: 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 the perpendicular line segments connecting the triangle sides with the exsymmedian points . (Wikipedia).
