Symmedian Point

A [b]symmedian point[/b] is a special point that is found in the interior of any triangle. It is located at the intersection of all three symmedians of the triangle. The symmedian point aligns with many special axes and circles found throughout the triangle. A [i]symmedian[/i] is a line segment created when one reflects a median across an angle bisector of a triangle. The symmedians in this picture are represented in black. A [i]median[/i] is a line segment whose endpoints are one angle’s vertex and the midpoint of the opposite side of the triangle. The medians in this picture are represented in [color=#0a971e]green[/color]. An [i]angle bisector[/i] is a ray that bisects an angle. The angle bisectors in this picture are represented in [color=#c51414]red[/color].

Which point on this picture represents the [b]symmedian point[/b]? What happens to the [b]symmedian point[/b] when the vertices of the triangle are moved? How would one find the [i]centroid[/i]? How would one find the [i]incenter[/i]?