Question Number 52506 by ajfour last updated on 09/Jan/19
Commented by ajfour last updated on 09/Jan/19
$${Find}\:{radii}\:{of}\:{both}\:{circles}\:{in}\:{terms} \\ $$$${of}\:{a}\:{and}\:{b}. \\ $$
Answered by mr W last updated on 09/Jan/19
$$\left({R}−{a}\right)^{\mathrm{2}} ={R}\left({R}−{b}\right) \\ $$$${R}^{\mathrm{2}} −\mathrm{2}{aR}+{a}^{\mathrm{2}} ={R}^{\mathrm{2}} −{bR} \\ $$$$\left(\mathrm{2}{a}−{b}\right){R}={a}^{\mathrm{2}} \\ $$$$\Rightarrow{R}=\frac{{a}^{\mathrm{2}} }{\mathrm{2}{a}−{b}} \\ $$$$ \\ $$$$\mathrm{2}{R}−\mathrm{2}{r}={b} \\ $$$$\Rightarrow{r}={R}−\frac{{b}}{\mathrm{2}} \\ $$$$\Rightarrow{r}=\frac{{a}^{\mathrm{2}} }{\mathrm{2}{a}−{b}}−\frac{{b}}{\mathrm{2}} \\ $$
Commented by ajfour last updated on 09/Jan/19
$${Best}\:{way}\:{Sir},\:{thanks}\:{a}\:{lot}! \\ $$