Triangle knowing two sidelines rb, rc and the Euler line re

1) The vertex A is the intersection between rb and rc
2) Let rb', rc' be the reflections of re with respect to rb and rc
3) Let D be the intersection between rb' and rc'
4) The perpendicular bisector of AD cuts re at O
5) The circle through A centered at O cuts rc at B and rb at C, and ABC is the requested triangle