For a given pivot P which is not H, there is one and only one circular pK whose pole Ω is the barycentric product P x igP. When P = H, all the circular pKs form a pencil of cubics. See details in the pages CL019 and CL035. The following table gives a selection of such circular pKs.
 P centers on the cubic cubic X1 X1, X15, X16, X36, X58, X106, X202, X203, X214, X758, X1130 K206 X2 X2, X3, X6, X67, X111, X187, X468, X524, X1560 K043 X3 X3, X15, X16, X35, X36, X54, X74, X186, X1154, X1511 K073 X4 see CL019 X5 X3, X5, X13, X14, X195, X1157, X1173 K067 X6 X6, X23, X111, X251 pK(X6 x X23, X6) X7 X1, X7, X57, X527, X1155, X1156, X1323 K949 X8 X1, X8, X40, X104, X519, X1145, X1319, X1339 K338 X9 X1, X9, X165, X1174, X2078, X2291 pK(X9 x X2078, X9) X13 X13, X14, X15, X16, X17, X62, X532, X619, X2381 K261a X14 X13, X14, X15, X16, X18, X61, X533, X618, X2380 K261b X21 X1, X3, X21, X759, X1175, X2074 pK(X21 x X5172, X21) X22 X3, X22, X23, X159, X1176, X1177 X23 X3, X6, X23, X25, X111, X187, X1177, X2393 K108 X30 see the Neuberg cubic page K001 X67 X2, X67, X141, X524 K103 X69 X2, X20, X69, X468, X524, X2373 pK(X524, X69) X74 X3, X15, X16, X74 K114 X76 X76, X83, X98, X732, X1670, X1671, X1691 K653 X79 X1, X13, X14, X79, X484 X80 X1, X10, X13, X14, X80, X484, X519, X759, X1128, X1168 K058 X98 X3, X98, X485, X486, X1687, X1688, X2065 K336 X104 X1, X3, X36, X90, X104, X912, X1795 K436 X111 X3, X6, X111, X187, X895, X6091, X8681, X8770, X15387, X15390, X15398 pK(X14908, X111) X230 X4, X487, X488 X232 X4, X114, X371, X372, X511, X2009, X2010 K337 X265 X4, X5, X13, X14, X30, X79, X80, X265, X621, X622, X1117, X1141 K060 X316 X2, X4, X67, X69, X316, X524, X671, X858, X2373 K008 X468 X2, X4, X126, X193, X468, X524, X671, X2374 K209 X512 X1, X99, X512, X2142, X2143 K021 X513 X1, X100, X513, X1054 K661 X515 X1, X36, X40, X80, X84, X102, X515 K269 X518 X1, X105, X518, X1282 X522 X1, X109, X522, X1768 X524 X1, X2, X6, X111, X524, X2930, X5524, X5525, X7312, X7313, X8591, X13574} X527 X1, X9, X57, X527, X2291 X616 X15, X16, X532, X616, X618 K438a X617 X15, X16, X533, X617, X619 K438b X621 X13, X14, X18, X533, X616, X619, X621, X628 K066b X622 X13, X14, X17, X532, X617, X618, X622, X627 K066a X647 X4, X122, X520, X1301 X650 X4, X123, X521 X671 X2, X4, X6, X23, X111, X524, X671, X895 K273 X698 X1, X194, X698, X699 X736 X1, X32, X76, X736, X737 X744 X1, X31, X75, X744, X745 X858 X2, X3, X66, X524, X858, X895 pK(X3, X858) X895 X6, X25, X64, X111, X895, X2393 pK(X895 x X25, X895) X1138 X15, X16, X30, X1138, X1511 X1141 X3, X13, X14, X54, X96, X265, X539, X1141, X1157 K112 X1156 X1, X9, X55, X1155, X1156, X2291 K950 X1157 X15, X16, X54, X195, X252, X1157 X1263 X4, X15, X16, X54, X140, X1263, X2070 K439 X1300 X3, X4, X186, X254, X1300 X1320 X1, X56, X84, X106, X517, X1320 pK(X9456, X1320) X1325 X3, X28, X36, X60, X65, X267, X501, X759, X1325, X2949 K340 X1503 X1, X20, X64, X147, X1297, X1503 X1886 X4, X118, X516, X917 X1916 X32, X39, X511, X733, X1676, X1677, X1916 pK(X9468, X1916) X1990 X4, X13, X14, X30, X113, X1300 K059 X2373 X2, X3, X23, X69, X524, X1177, X2373 K113 X3065 X1, X15, X16, X35, X3065, X3467, X3647, X5127, X5131, X7343, X15792 X3448 X523, X3448, X6328, X14086 K878 X5080 X4, X12, X21, X72, X80, X191, X502, X758, X5080 K720