User:Handgiver/Lemoine Circles

In plane geometry, given a triangle ABC and located his Lemoine point K, Lemoine parallel lines determine on the sides of Triangle six points that belong to a itself Disk (mathematics) called first Lemoine Circle.

Instead if we consider Antiparallel (mathematics) at the three triangle sides passing by K, these intersect all triangle sides in six sides that belong to a Disk (mathematics), called Second Lemoin Circle

These two circles are called in honour of French mathematician Émile Lemoine (1840-1912).

First Lemoine Circle Properties

• Given a triangle ABC and its orthic triangle XYZ, the points U, U ', V, V', W, W ', determined by the intersection of the straight lines passing through the midpoints of the sides of the nettle triangle with the sides of the fundamental triangle ABC, belong to the same circle, that is to the first circle of Lemoine.

• Given a triangle ABC, the six points that are on the first circle of Lemoine are the vertices of a Hexagon, named Lemoine hexagon.

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