HYACINTHOS 20367

Dear All My Friends,

It is well known that some lines passing Symmedian Point K intersect side lines of
reference triangle ABC to generate first and second Lemoine
circles.

It is interesting that we can use some
circles passing Symmedian Point K
to generate a circle too. Detail as following:

In reference triangle ABC, K is Symmedian Point, O is
circumcenter.
We construct a circle passing A, K with center on line AO.
Other than A, this circle intersects AB, AC at Ab, Ac respectively. Similarly
construct Bc, Ba, Ca, Cb.

Result: six points Ab, Ac, Bc, Ba, Ca, Cb are concyclic on a
circle centered at X(575).

Dear All My Friends,

If this circle is well known?

Thank you and best regards,
Bui Quang Tuan