Taking arc A first: Your desired radius is 58 units. Offset each of the two circles you're connecting by 58. Draw a new circle, of radius 58, at the intersection of the two new circles. Delete the offset circles and trim the R58 circle to tidy up.
For arc B you essentially take the same process, the difference being that one of the elements you're filleting is a line. Ensure your line extends beyond the likely centrelpoint of the fillet circle. I'd have it touching the right-hand cirlce (with R52). Offset your line and circle by 45 units (the desired fillet radius). Draw a new circle of radius 45 centred on the intersection of the new line and circle. Trim to tidy.