Triangle given the vertex A, the circumcenter O and the symmedian point K

1) Let A' be the intersection between AK and the circumcircle (circle with center O through A).
2) Take D in Ak such that the double ratio  {AA'KD} = -3.
3) The tangents through D to the circumcircle have as contact points the vertices B and C.
An alternative construction is c11.