Let P, P* be two isogonal points; let A'B'C' be the pedal triangle of P. Let Pa, Pb, Pc be the isogonals of P with respect to AB'C', BC'A', CA'B'. The three circles {PaB'C'}, {PbC'A'}, {PcA'B'} and also the three circles {A'PbPc}, {B'PcPa}, {C'PaPb} have a common point.