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  • Two circles whose distance between two centres is   are touching each externally at

Two circles whose distance between two centres is \frac{20}{3}  are touching each externally at (1,1). If their direct common tangents intersect at (5,4) then the ratio of radius of bigger circle to smaller circle is
 

Option: 1

3


Option: 2

5


Option: 3

\frac{5}{3}


Option: 4

\frac{5}{2}


Answers (1)

best_answer

\begin{aligned} &\text{Let }\mathbf{r}_1>\mathbf{r}_2\\ & r_1+r_2=\frac{20}{3} \quad--(1) \\ & \frac{r_2}{C_2 P}=\frac{r_1}{C_1 P} \Rightarrow \frac{r_2}{5-r_2}=\frac{r_1}{5+r_1} \quad--(2)\\ &\text{solving(1)\&(2) we get }\mathbf{r}_1=5, \mathrm{r}_2=\frac{5}{3} \end{aligned}

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