Gergonne Point
The Gergonne Point can be found as follows. First, find the incenter (concurrence of angle bisectors). Then, draw perpendicular lines to the edges of the triangle from the incenter. Make a circle through the points made by the intersections of the perpendicular lines and the edges of the triangle. This is called the incircle, as it is tangent to all the edges (touches them at only one point - the one found earlier). Draw lines from the vertices to the opposite intersection of edge and incircle. These intersect at the Gergonne Point.