The Lucas circles can be drawn by inscribing a square in this other geometric shape. Clark Kimberling has catalogued over three thousand centers of this shape, some of which include the Nagel point and the nine-point center. Kimberling center X1 refers to the point at which the angular bisectors intersect; that point does not necessary lie on the Euler line, unlike the (*) circumcenter, orthocenter, and centroid. For 10 points, name this geometric shape whose angles add up to one hundred eighty 
The Lucas circles can be drawn by inscribing a square in this other geometric shape. Clark Kimberling has catalogued over three thousand centers of this shape, some of which include the Nagel point and the nine-point center. Kimberling center X1 refers to the point at which the angular bisectors intersect; that point does not necessary lie on the Euler line, unlike the (*) circumcenter, orthocenter, and centroid. For 10 points, name this geometric shape whose angles add up to one hundred eighty degrees and has three sides.
The Lucas circles can be drawn by inscribing a square in this other geometric shape.
{triangle}