Question

The sum of the area of two circles which touch each other externally is 153$\pi$. 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

Answer 1

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

$r_1^2+r_2^2+2r_1{r}_2=225$

$2r_1{r}_2=225-153$

$r_1{r}_2=36$

$r_1–r_2=\sqrt{(r_1^2+r_2^2{)}^2-4r_1{r}_2}=\sqrt{225-144}=9$

$⟹r_1=12,r_2=3$

$⟹\frac{r_1}{r_2}=4$