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10-1.Circle and System of Circles
medium
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
A
Circles touch each other internally
B
Circles touch each other externally
C
Circles intersect at two distinct points
D
None of these
Solution
(a) ${r_1} = \sqrt {{g^2} + {f^2} – c} = 12$
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.
Standard 11
Mathematics
