Symmedian of a triangle| Definition and Examples

The symmedian of a triangle is a geometric concept related to the medians of a triangle. Given a triangle ABC, the symmedian of the triangle is a line segment that divides one of the angles into two parts in such a way that the ratio of the lengths of the two line segments on either side of the angle is equal to the ratio of the lengths of the adjacent sides. More precisely, let AD be the symmedian of triangle ABC, where D lies on side BC. Then, according to the symmedian property: