Triangle knowing the vertex A and the Brocard points V, W

1) Let O be the circumcenter of AVW
2) Let S be the reflection of A in the midpoint of VW
3) The perpendicular from S to AO cuts AV at M and VW at L
4) Let A' be the reflection of A in the midpoint of MW
5) The circle through A' centered at M cuts the conic {AWLMA'} at A' and B
6) The isogonal line of AB with respect to AVW cuts BL at C, and ABC is the requested triangle.