The Fuhrmann Circle
Suppose the circumference is drawn around triangle ABC and X', Y', and Z' are the midpoints of the arcs cut off by the sides. Now suppose that each of these midpoints is reflected in the nearest side of the triangle. Then the triangle of images XYZ and its circumcircle are called the Fuhrmann triangle and the Fuhrmann circle of triangle ABC, after the 19th-century German geometer Wilhelm Fuhrmann (1833-1904). See figure 1 above.
Click here for a GSP sketch of the Fuhrmann Circle that can be used for investigations.
An interesting point:
The Fuhrmann circle goes through at least 8 points of the nine-point circle of a triangle.
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