(A) The first circle lies in the first quadrant and touches both axes,so its centre $C_1$ is $(12, 12)$ and its radius $r_1 = 12$.The second circle ha

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Circles touch each other internally

(A) The first circle lies in the first quadrant and touches both axes,so its centre $C_1$ is $(12, 12)$ and its radius $r_1 = 12$.The second circle has centre $C_2 = (8, 9)$ and radius $r_2 = 7$.The distance between the centres $C_1$ and $C_2$ is given by $d = \sqrt{(12 - 8)^2 + (12 - 9)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.The difference between the radii is $|r_1 - r_2| = |12 - 7| = 5$.Since the distance between the centres $d = |r_1 - r_2|$,the circles touch each other internally.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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