A) Circles touch each other internally
B) Circles touch each other externally
C) Circles intersect at two distinct points
D) None of these
Correct Answer: A
Solution :
\[{{r}_{1}}=\sqrt{{{g}^{2}}+{{f}^{2}}-c}=12\] Also \[r=-g=-f=12\] (because it touches both the axes) \[\Rightarrow {{C}_{1}}=(12,\ 12),\ {{r}_{2}}=7,\ {{C}_{2}}=(8,\ 9)\] Now \[{{C}_{1}}{{C}_{2}}=5\] and \[{{r}_{1}}-{{r}_{2}}=5\] Therefore, circles touch each other internally.
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