If the circles x^2 + y^2 = a^2 and x^2 + y^2 | vedclass

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(D) The first circle $x^2 + y^2 = a^2$ has center $C_1 = (0, 0)$ and radius $r_1 = a$.The second circle $x^2 + y^2 - 2gx + g^2 - b^2 = 0$ can be rewri

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$g = a + b$

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(D) The first circle $x^2 + y^2 = a^2$ has center $C_1 = (0, 0)$ and radius $r_1 = a$.The second circle $x^2 + y^2 - 2gx + g^2 - b^2 = 0$ can be rewritten as $(x - g)^2 + y^2 = b^2$,which has center $C_2 = (g, 0)$ and radius $r_2 = b$.Two circles touch each other externally if the distance between their centers is equal to the sum of their radii,i.e.,$d(C_1, C_2) = r_1 + r_2$.The distance between $C_1(0, 0)$ and $C_2(g, 0)$ is $\sqrt{(g - 0)^2 + (0 - 0)^2} = |g|$.Thus,$|g| = a + b$. Assuming $g, a, b > 0$,we get $g = a + b$.

If the circles $x^2 + y^2 = a^2$ and $x^2 + y^2 - 2gx + g^2 - b^2 = 0$ touch each other externally,then:

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