Verified answer

[tex]\displaystyle \sf x^2+y^2-2x-4y+k=0 \\\\ \text{o ponto ( 2 , 1 ) pertence {\`a} circunfer{\^e}ncia, ent{\~a}o } : \\\\ 2^2+1^2-2\cdot 2-4\cdot 1+k = 0 \\\\ 4+1-4-4+k = 0 \\\\ \huge\boxed{\sf k = 3 }\checkmark[/tex]