For some reason I can't upload the worksheet.
It is just the 3,4,5 triangle.

restart

sph:=(x-3)^2+(y-7)^2+(z-4)^2-25

plxy:=z=0
plyz:=x=0
ctr:=[3,7,4]
R:=5
ctrplxy:=[3,7,0]
4^2+Rxy^2=5^2
fsolve( ?? );
Rxy:=3
ctrplyz:=[0,7,4]
3^2+Ryz^2=5^2

fsolve( ?? );
Ryz:=4
#Center  and Radius on xy plane
ctrplxy;
Rxy
#Center  and Radius on yz plane
ctrplyz;
Ryz

This is just a quick test. I drew it in a CAD system to see. And  another possible assumption is the side slopes are equal.

On my pc Maple docs are here. Or are you asking about windows File History?