In[]:=
$Version
Out[]=
15.0.1 for Linux x86 (64-bit) (July 2, 2026)
In[]:=
ClearAll["`*"];Remove["`*"];
In[]:=
Reduce[t>0&&ForAll[{x,y},x>0&&y>0&&xy==6,(x+y+t)^2==(x-a)^2+(y-b)^2],{a,b,t},Reals]
Out[]=
a-2
3
&&b-2
3
&&t2
3