Circle And System Of Circles Question 292
Question: A circle with radius 12 lies in the first quadrant and touches both the axes, another circle has its centre at (8,9) and radius 7. Which of the following statements is true
Options:
A) Circles touch each other internally
B) Circles touch each other externally
C) Circles intersect at two distinct points
D) None of these
Show Answer
Answer:
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_1C_2=5 $ and $ r_1-r_2=5 $
Therefore, circles touch each other internally.
BETA
