The two circles x2+y2=c2(c>0) touch each other if:
We have,
As centre of one circle is (0,0) and other circle passes through the (0,0).
Therefore,
Also C1(a2,0) and C2(0,0).
Then,
r1=a2r2=c
⇒C1C2=r1−r2=a2
⇒C=a2=a2
C=a
If two circles touches each other they must be touch each other internally.