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.
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