Triangle knowing two sidelines rb, rc and the Gergonne point Ge

1) The vertex A is the intersection between rb and rc
2) Inscribe a circle in the quadrant formed by rb and rc and containing Ge.
3) This circle cuts AGe at T
4) The tangent at T to the circle cuts rb, rc at B', C'
5) Let Ge' be the Gergonne point of AB'C'
6) The requested triangle is the homothetic of AB'C' with center A and ratio AGe/AGe'