Question Number 196021 by universe last updated on 16/Aug/23
Answered by mr W last updated on 17/Aug/23
Commented by mr W last updated on 17/Aug/23
$$\mathrm{3}\:{triangles}\:{are}\:{similar}. \\ $$$$\frac{{AC}}{{BC}}=\frac{\mathrm{12}}{\mathrm{16}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${AC}^{\mathrm{2}} +{BC}^{\mathrm{2}} ={a}^{\mathrm{2}} \\ $$$$\Rightarrow{AC}=\frac{\mathrm{3}{a}}{\mathrm{5}},\:{BC}=\frac{\mathrm{4}{a}}{\mathrm{5}} \\ $$$$\frac{{r}}{\mathrm{12}}=\frac{{a}}{{BC}}=\frac{\mathrm{5}{a}}{\mathrm{4}{a}} \\ $$$$\Rightarrow{r}=\mathrm{15}\:\checkmark \\ $$