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For a given pivot P which is not H, there is one and only one circular pK. 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

pK(X5 <> X1157, X5)

X6

X6, X23, X111, X251

 

X7

X1, X7, X57, X527, X1155, X1156, X1323

pK(X7 <> X1155, X7)

X8

X1, X8, X40, X104, X519, X1145, X1319, X1339

K338

X9

X1, X9, X165, X1174, X2078, X2291

pK(X9 <> 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 <> ?, X21)

X22

X3, X22, X23, X159, X1176, X1177

 

X23

X3, X6, X23, X25, X111, X187, X1177, X2393

K108

X30

X1, X3, X4, X13, X14, X15, X16, X30, X74, X399, X484, X616, X617, X1138, X1157, X1263, X1276, X1277, X1337, X1338, X2132, X2133

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

pK(X104 <> X3, X104)

X111

X3, X6, X111, X187, X895

 

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

 

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<>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

pK(X1156 <> X55, X1156)

X1157

X15, X16, X54, X195, X252, X1157

 

X1263

X4, X15, X16, X54, X140, X1263, X2070

pK(X1263 <> X54, X1263)

X1300

X3, X4, X186, X254, X1300

 

X1320

X1, X56, X84, X106, X517, X1320

pK(X1320 <> X56, 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(X1916 <> X32, X1916)

X1990

X4, X13, X14, X30, X113, X1300

K059

X2373

X2, X3, X23, X69, X524, X1177, X2373

K113

X5080

X4, X12, X21, X72, X80, X191, X502, X758, X5080

pK(X37, X5080)