[lqwtcytv] Elder Wand of a triangle

Let the line from a triangle vertex to the tangent point of the incircle on the opposite edge be named henceforth the Elder Wand (joining the Witch of Agnesi among geometric objects with interesting names).

The three altitudes of a triangle intersect at the orthocenter.
The three medians of a triangle intersect at the centroid.
The three angle bisectors of a triangle intersect at the incenter.
The three perpendicular bisectors of a triangle intersect at the circumcenter.
The three symmedians of a triangle intersect at the symmedian point.
The three splitters of a triangle intersect at the Nagel point.
The three Elder Wands of a triangle intersect at the Gergonne point.

Inspired by

math-fail.com

which is in turn inspired by the Deathly Hallows symbol in Harry Potter.