A circle C₁ of radius 2 touches both x -axis and y -axis. Another circle C₂ whose radius is grea

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10-1.Circle and System of Circles

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A circle $C_1$ of radius $2$ touches both $x$ -axis and $y$ -axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is-

A

$6 - 4 \sqrt 2$

B

$6 + 4 \sqrt 2$

C

$6 - 4 \sqrt 3$

D

$6 + 4 \sqrt 3$

Solution

$\mathrm{OA}^{2}=2 \mathrm{r}^{2}=(\mathrm{OC}+\mathrm{CA})^{2}$

$2 r^{2}=O C^{2}+C A^{2}+2 . O C \cdot C A$

$2 r^{2}=8+(r+2)^{2}+2.2 \sqrt{2}(r+2)$

By solving this eq.

$r=6+4 \sqrt{2}$

Standard 11

Mathematics

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