Circles Part 1

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
Centers of each other lies on circumference of each other.
Hence, (b) is incorrect statement.