Point with cevian triangle similar to the pedal triangle of a point M

1) Let GaGbGc be the antimedial triangle
2) The circle through M and tangent to AB at A cuts AC at A1
3) The circle through M and tangent to AC at A cuts AB at A2
4) Draw analogously B1, B2, C1, C2
5) The conics {BCGaA1A2}, {CAGbB1B2}, {ABGcC1C2} intersect at the requested point P.