# Feuerbach Action! (GoGeometry Action 167)

- Author:
- Tim Brzezinski

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?**