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The length of the direct common tangent to two circles of radii $$r_1$$ and $$r_2$$ and is the distance between their centres is:
$$\sqrt{d^2(r_1r_2)}$$
$$\sqrt{d^2 - (r_1^2r_2^2)}$$
$$\sqrt{d^2 - (r_1 + r_2)^2}$$
$$\sqrt{d^2 - (r_1 - r_2)^2}$$
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