Question Number 189942 by Rupesh123 last updated on 24/Mar/23
Answered by mr W last updated on 24/Mar/23
$$\mathrm{2}{R}={a}+\mathrm{2}{r}+{b} \\ $$$$\Rightarrow{R}=\frac{{a}+{b}}{\mathrm{2}}+{r} \\ $$$$\sqrt{\left({R}−{r}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} }={R}−{r}−{b} \\ $$$$\sqrt{\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} }=\frac{{a}−{b}}{\mathrm{2}} \\ $$$${r}^{\mathrm{2}} =\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{{a}−{b}}{\mathrm{2}}\right)^{\mathrm{2}} ={ab} \\ $$$$\Rightarrow{r}=\sqrt{{ab}} \\ $$
Commented by Rupesh123 last updated on 24/Mar/23
Perfect ��
Commented by Skabetix last updated on 12/Apr/23
Commented by Skabetix last updated on 12/Apr/23
$${an}\:{other}\:{solution}\:{in}\:{french} \\ $$