Two circles have radii 14 cm and 6 cm. If the length of a direct common tangent is 24 cm, what is the distance between their centers?

Question

Accepted Answer

1. Let the radii be $r_1=14$ and $r_2=6$. The tangent length is $L=24$.  
2. For a direct common tangent: $L=\sqrt{d^2-(r_1-r_2)^2}$, where $d$ is the center distance.  
3. So $24^2=d^2-(14-6)^2$, i.e. $576=d^2-8^2$. Thus $d^2=576+64=640$.  
4. Hence $d=\sqrt{640}=8\sqrt{10}$. Choose option **(b)**.  
FINAL_ANSWER: b

Answer

Answer

Answer