Question Number 208049 by mr W last updated on 03/Jun/24
Commented by Frix last updated on 03/Jun/24
$${a}=\mathrm{1}\wedge{b}=\mathrm{3} \\ $$$${r}={a}+{b}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }=\mathrm{4}−\sqrt{\mathrm{10}} \\ $$
Answered by mr W last updated on 03/Jun/24
Commented by mr W last updated on 03/Jun/24
$${AB}={c}=\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$$${R}=\frac{{c}}{\mathrm{2}}=\frac{\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{\mathrm{2}} \\ $$$$\left({r}−\frac{{a}}{\mathrm{2}}\right)^{\mathrm{2}} +\left({r}−\frac{{b}}{\mathrm{2}}\right)^{\mathrm{2}} =\left({R}−{r}\right)^{\mathrm{2}} \\ $$$$ \\ $$$${r}−\left({a}+{b}−\mathrm{2}{R}\right)=\mathrm{0} \\ $$$$\Rightarrow{r}={a}+{b}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$
Commented by Tawa11 last updated on 21/Jun/24
$$\mathrm{weldone}\:\mathrm{sir} \\ $$