symmedian
A symmedian of a triangle is a line through a vertex that is the isogonal conjugate of the corresponding median. Equivalently, it is obtained by reflecting the median across the angle bisector at the same vertex. For example, the A-symmedian is the line through A that is the isogonal image of the A-median.
If the A-symmedian meets BC at a point K, then the division of BC satisfies BK/CK = AB^2/AC^2.
The three symmedians of triangle ABC are concurrent at a single interior point, known as the symmedian