- Nov 6 4:02 AMand the perpendicular to C-median at G, and define Ba and Cb cyclically.cyclically. Let Ac be the intersection of the perpendicular bisector of AGbisector of AG and the perpendicular to B-median at G, and define Bc, CaLet ABC be a triangle, and let Ab be the intersection of the perpendicularEquivalently:Let ABC be a triangle, and let Ab be the center of the circle through A andtangent to the B-median, and define Bc and Ca cyclically. Let Ac be the center

of the circle through A and tangent to the C-median, and define Ba and Cb cyclically.

The points Ab, Ba, Bc, Cb, Ca, Ac lie on a circle, of which X(5569) is the center,

(Dao Thanh Oai, Nov. 3, 2013)

The points Ab, Ba, Bc, Cb, Ca, Ac lie on a circle, of which X(5569) is the center,The circles (Ab), (Ac), (Bc), (Ba), (Ca), (Cb) concur at GGeneralizationLet ABC be a triangle and Gat, Gbt, Gct three points on AG,BC,CG, resp.

such that:GatA / GatG = GbtB / GbtG = GctC / GctG. = t

Let Ab be the intersection of the perpendicular to AG at Gat and the

perpendicular to B-median at G. and define Bc, Ca cyclically. Let Ac be the

intersection of the perpendicular to AG at Gat and the perpendicular to C-median

at G, and define Ba and Cb cyclically. The points Ab, Ba, Bc, Cb, Ca, Ac lie on

a circle.Locus: Which is the center of the circle as t varies?APHIn the attached figure t = 1/3