Question Number 81135 by ajfour last updated on 09/Feb/20
Commented by ajfour last updated on 09/Feb/20
$${Find}\:{radii}\:{of}\:{both}\:{circles}. \\ $$
Answered by mr W last updated on 09/Feb/20
$$\left({R}−{b}\right)\left({R}−{c}\right)=\left({R}−{a}\right)^{\mathrm{2}} \\ $$$${bc}−{a}^{\mathrm{2}} =\left({b}+{c}−\mathrm{2}{a}\right){R} \\ $$$$\Rightarrow{R}=\frac{{bc}−{a}^{\mathrm{2}} }{{b}+{c}−\mathrm{2}{a}} \\ $$$$\mathrm{2}{r}+{b}+{c}=\mathrm{2}{R} \\ $$$$\Rightarrow{r}={R}−\frac{{b}+{c}}{\mathrm{2}}=\frac{{bc}−{a}^{\mathrm{2}} }{{b}+{c}−\mathrm{2}{a}}−\frac{{b}+{c}}{\mathrm{2}} \\ $$
Commented by ajfour last updated on 10/Feb/20
$${thanks}\:{sir},\:{it}\:{was}\:{boneless}! \\ $$