<s>[INST] Find the equation of the circle. Find the equation of the circle whose radius is $5$ which touches the circle $x^2 + y^2 - 2x -4y - 20 = 0$ externally at the point $(5,5)$
 [/INST] HINT:
$(x-a)^2+(y-b)^2=5^2$ will touch  $(x-1)^2+(y-2)^2=5^2$
iff $5+5=\sqrt{(a-1)^2+(b-2)^2}$
Again, $(a,b), (1,2), (5,5)$ are collinear.
So, we have two equations with two unknowns 
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