Four congruent circles, three tangent to two sides and the fourth tangent to them

1) Let P be the reflection of the ninecenter N in the Feuerbach point F.
2) Let M be the midpoint between A and the circumcenter O.
3) The parallel from F to PM cuts IM (I the incenter) at Ta.
4) The parallel from Ta to OA cuts IO at Od and IA at Oa.
5) The circles centered at Od, Oa going through Ta are two of the four requested.
6) The parallel from Oa to AB cuts IB at a new center Ob, and Oc is constructed analogously.