Lamoen circle

Lamoen circle

The term Lamoen circle comes from triangular geometry . It goes back to a discovery by the Dutch artist Floor van Lamoen in 2000.

The center points of the six sub-triangles into which a given triangle is divided by its bisectors lie on a circle .

Focus

The center of the Lamoen circle has the Kimberling number X (1153). Its barycentric coordinates are:

${\displaystyle 10a^{4}+4(b^{4}+c^{4})-10b^{2}c^{2}-13a^{2}(b^{2}+c^{2})\,}$

${\displaystyle 10b^{4}+4(a^{4}+c^{4})-10a^{2}c^{2}-13b^{2}(a^{2}+c^{2})\,}$

${\displaystyle 10c^{4}+4(a^{4}+b^{4})-10a^{2}b^{2}-13c^{2}(a^{2}+b^{2})\,}$

See also: Distinguished Points in the Triangle

literature

• F. van Lamoen: Problem 10830 . In: American Mathematical Monthly , 107, 2000, p. 863.

Web links

• Eric W. Weisstein : van Lamoen Circle . In: MathWorld (English).
• Lamoen circle - a visualization with GeoGebra