Question Number 84304 by Wepa last updated on 11/Mar/20
$$\Delta\mathrm{ABC}\:\mathrm{AB}=\mathrm{a}\:\mathrm{BC}=\mathrm{b}\:\mathrm{AC}=\mathrm{c}\: \\ $$$$\mathrm{and}\:\angle\mathrm{C}=\mathrm{90}° \\ $$$$\mathrm{r}=? \\ $$
Commented by mr W last updated on 11/Mar/20
$${r}=\frac{{ab}}{{a}+{b}+{c}} \\ $$
Answered by $@ty@m123 last updated on 11/Mar/20
$${General}\:{formula}: \\ $$$${r}=\frac{\bigtriangleup}{{s}},\:\bigtriangleup=\frac{\mathrm{1}}{\mathrm{2}}{ab}\mathrm{sin}\:{C} \\ $$$${Here}\:{C}=\mathrm{90}^{\mathrm{o}} \\ $$$$\therefore\:{r}=\frac{{ab}\mathrm{sin}\:\mathrm{90}^{\mathrm{o}} }{\mathrm{2}×\frac{{a}+{b}+{c}}{\mathrm{2}}} \\ $$$$\Rightarrow\:{r}=\frac{{ab}}{{a}+{b}+{c}} \\ $$