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
B
2
C
3
D
None of these

Solution

## The correct option is A 4Let $$r_1$$ 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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