Circle tangent to BC and externally tangent to the B- and C- excircles

1) The B- and C- excircles touch BC at Ab, Ac.
2) Draw the circle with diameter AbAc.
3) This circle cuts the A-altitudeat M1, M2.
4) The line joining the excenters Eb, Ec cuts BC at Z.
5) The circle centered at Z and going through M1, M2 cuts BC at X.
6) The line L1 perpendicular to BC at X and the radical axis L2 between the B- and C- excircles intersect at Y.
7) The requested circle has diameter XY.