Feuerbach Action! (GoGeometry Action 167)

Creation of this resource was inspired by a problem posted by Antonio Gutierrez. The FEUERBACH POINT of a triangle is the point at which the triangle's incircle (shown in black below) intersects the triangle's 9-Point Circle (shown in blue). In the applet below, the Feuerbach point is the pink point. The 3 turquoise points are the points at which the triangle's 9-point circle intersects the triangles sides. These 3 turquoise points are actually the midpoints of the sides of this triangle. The triangle's 3 (white) vertices are moveable. The green slider controls the size of the interior angle with green vertex. Interact with this applet below for a few minutes. How can we formally prove the phenomenon dynamically illustrated here?