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?