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The sum of the areas of two circles, which touch each other externally, is $$153\pi$$. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.
Given:
$$\pi((r_1)^2 + (r_2)^2) = 153\pi$$
So
$$(r_1)^2 + (r_2)^2 = 153$$
Or $$((r_1) + (r_2))^2 - 2(r_1)(r_2) = 153$$
Or $$(r_1)(r_2) = 36$$ and $$(r_1) + (r_2) = 15$$
$$r_1 = 12$$
$$r_2 = 3$$
Ratio = 4
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