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The Lester circle is the circle on which the circumcenter C, nine-point center N, and the first and second Fermat points X and X^' lie (Kimberling 1998, pp. 229-230). Besides ...

The Mandart circle is the circumcircle of the extouch triangle. It has center at Kimberling center X_(1158), which has trilinear center function (1) and radius ...

Given a point P and a triangle DeltaABC, the Miquel triangle is the triangle DeltaP_AP_BP_C connecting the side points P_A, P_B, and P_C of DeltaABC with respect to which M ...

The Moses circle is defined as the circle with center at the Brocard midpoint X_(39) that is tangent to the nine-point circle at the center of the Kiepert hyperbola X_(115). ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

The orthocentroidal circle of a triangle DeltaABC is a central circle having the segment joining the triangle centroid G and orthocenter H of DeltaABC as its diameter ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

Given a parabola with parametric equations x = at^2 (1) y = 2at, (2) the negative pedal curve for a pedal point (x_0,0) has equation x_n = (at^2[a(3t^2+4)-x_0])/(at^2+x_0) ...

If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...

The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center X_(195), which is the ...