Consider Kimberling centers X_20 (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_468 (intersection L_E intersection L_O of the Euler line and orthic axis), X_650 (intersection L_G intersection L_0 of the Gergonne line and orthic axis), and X_1323 (Fletcher point; intersection L_G intersection L_S of the Gergonne line and Soddy line). Amazingly, these points are concyclic in a circle here dubbed the GEOS circle. The GEOS circle has rather complicated radius. Its center is the midpoint of X_650 and X_20 = Z, which has center function α = (a s_a)/((a - b)(c - a)) + (a^2 S_A - S_B S_C)/S^2, where s_a = (b + c - a)/2 and S, S_A, S_B, and S_C is Conway triangle notation, which is not a Kimberling center.
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