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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 ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

The Stammler circle is the circumcircle of the Stammler triangle. Unexpectedly, it has center at the circumcenter O (X_3) of the reference triangle and radius 2R (Ehrmann and ...

The Steiner circle is the central circle with center at the nine-point center X_5 and radius R_S=3/2R, where R is the circumradius of the reference triangle. It is the ...

The Steiner triangle DeltaS_AS_BS_C (a term coined here for the first time), is the Cevian triangle of the Steiner point S. It is the polar triangle of the Kiepert parabola. ...

The Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...

The symmedial triangle DeltaK_AK_BK_C (a term coined here for the first time), is the triangle whose vertices are the intersection points of the symmedians with the reference ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

Consider two directly similar triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 with B_1C_1:A_1C_1:A_1B_1=B_2C_2:A_2C_2:A_2B_2=a:b:c. Then a·A_1A_2, b·B_1B_2 and c·C_1C_2 form the ...

Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...