Circle And System Of Circles Question 300
Question: The condition that the circle $ {{(x-3)}^{2}}+{{(y-4)}^{2}}=r^{2} $ lies entirely within the circle $ x^{2}+y^{2}=R^{2}, $ is
[AMU 1999]
Options:
A) $ R+r\le 7 $
B) $ R^{2}+r^{2}<49 $
C) $ R^{2}-r^{2}<25 $
D) $ R-r>5 $
Show Answer
Answer:
Correct Answer: D
Solution:
Clearly, $ r_1-r_2>C_1C_2 $
$ r_1=R, $
$ C_1(3,,4); $
$ r_2=r; $
$ C_2(0,,0) $
$ R-r>\sqrt{{{(3-0)}^{2}}+{{(4-0)}^{2}}} $
therefore R - r > 5.
BETA
