If we draw lines passing through the symmedian K and parallels to the sides, these lines cut the sides at six points lying in a circle called the first Lemoine circle. Its center is the midpoint between K and the circumcenter O.
If we draw lines passing through the symmedian K and antiparallels to the sides, these lines cut the sides at six points lying in a circle called the second Lemoine circle. Its center is K.