So we have edges of almost 4.19...
and angles of : 149.1 degrees / 119.9 degrees / 91 degrees
radius = 0.87922379771..
Or:
we choose for edges: 4.1543544.. / 4.1982283.. / 4.1917588..
and angles: 90 degrees / 120 degrees / 150 degrees
radius = 0.8450378150..
Quite remarkable, isn't it ?!