Creation of this resource was inspired by a [url=http://gogeometry.com/center/feuerbach_point_facts_triangle.html]problem[/url] posted by [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]The [b][color=#ff00ff]FEUERBACH POINT[/color][/b] of a triangle is the point at which the triangle's [b]incircle (shown in black below)[/b] intersects the triangle's [b][color=#0000ff]9-Point Circle (shown in blue)[/color][/b]. [br][br]In the applet below, the [b][color=#ff00ff]Feuerbach point[/color][/b] is the [b][color=#ff00ff]pink point[/color][/b]. [br][br]The [b][color=#1e84cc]3 turquoise points[/color][/b] are the points at which the triangle's [b][color=#0000ff]9-point circle[/color][/b] intersects the triangles sides. [br]These [b][color=#1e84cc]3 turquoise points[/color][/b] are actually the [b][color=#1e84cc]midpoints of the sides of this triangle[/color][/b]. [br][br]The triangle's 3 (white) vertices are moveable. [br]The [b][color=#38761d]green slider[/color][/b] controls the size of the interior angle with [b][color=#38761d]green vertex[/color][/b]. [br][br]Interact with this applet below for a few minutes. [br][b]How can we formally prove the phenomenon dynamically illustrated here? [/b]