A circle with radius 12 lies in first quadrant and touches both axes, another circle has its centre

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10-1.Circle and System of Circles

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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

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