C1⇒x2+y2−10x−10y+41=0 (x−5)2+(y−5)2+41=25+25 ⇒ Centre =(5,5) and Radius =3 ⇒(x−5)2+(y−5)2=32 C2⇒x2+y2−16x−10y+80=0 (x−8)2+(y−5)2+80=64+25 ⇒(x−8)2+(y−5)2=32 ⇒ Centre =(8,5) and Radius =3 Now, distance between centres =√(8−5)2+(5−5)2=3
Average radii =
3+3
2
=3 ∴ Option (a) is correct. C1(8,5)=(8−5)2+(5−5)2−9=0 C2(5,5)=(5−8)2+(5−5)2−9=0 Centres of each other lies on circumference of each other. Hence, (b) is incorrect statement.