Question

Figure shown line $L=0$ which is radieal axis of $S_1=0$ and $S_2=0$. The direct common tangent touches circle $S_1=0$ and $S_2=0$ at $A$ and $B$ respectively and cuts $L=0$ at $P$. Let $\frac{Area\left(\Delta PA{C}_1\right)}{Area\left(\Delta PB{C}_2\right)}=2$ and radius of $S_2=0$ is $5$, if radius of $S_1=0$ is $r$ then the value of $\frac{r}{5}$ is ( $C_1$ and radius of $S_2=0$ is $5$, if radius of $S_1=0$ is $r$ then the value of $\frac{r}{5}$ is $C_1$ and $C_2$ are centres of $S_1=0$ and $S_2=0$

• A. 1
• B. 2
• C. 3
• D. 6

Answer 1

The correct option is B 2

Since $L=0$ is the radial axis of two circles then, $PA=PB$

Given, $\frac{Area△PA{C}_1}{Area△PB{C}_2}=2\frac{\frac{1}{2}\left(A{C}_1\right)\left(PA\right)}{\frac{1}{2}\left(B{C}_2\right)\left(PB\right)}=2$

Given, $B{C}_2=r=5$

$\frac{A{C}_1}{5}=2A{C}_1=r=10$

then, $\frac{r}{5}=\frac{10}{5}=2$