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Question

The sum of the area of two circles which touch each other externally is 153$$\displaystyle \pi $$. If the sum of their radii is 15, the ratio of the larger to the smaller radius is


A
4
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B
2
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C
3
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D
None of these
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Solution

The correct option is A 4

Let $$r_1$$ and $$r_2$$ be the radii:

Given $$A_1 + A_2 = 153 \pi$$

$$\pi r_1^2 + \pi r_2^2 = 153 \pi$$

$$r_1^2 + r_2^2 = 153 $$

And

$$r_1 + r_2 = 15$$

SOBS

$$r_1^2 + r_2^2 + 2r_1r_2 = 225$$

$$2r_1r_2 = 225 - 153$$

$$r_1r_2 = 36$$

$$r_1 – r_2 = \sqrt{(r_1^2 + r_2^2)^2 - 4r_1r_2} = \sqrt{225 - 144} = 9$$

$$\implies r_1 = 12 , r_2 = 3$$

$$\implies \dfrac{r_1}{r_2} = 4$$


Mathematics

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