Question Number 165272 by cortano1 last updated on 28/Jan/22
Answered by ajfour last updated on 28/Jan/22
$$\mathrm{2}{a}=\mathrm{10}{cm} \\ $$$${a}^{\mathrm{2}} =\left(\mathrm{2}{r}−\mathrm{2}{a}\right)\left(\mathrm{2}{a}\right) \\ $$$${r}=\frac{\mathrm{5}{a}}{\mathrm{4}}=\frac{\mathrm{5}}{\mathrm{8}}\left(\mathrm{10}{cm}\right)=\mathrm{6}.\mathrm{25}{cm} \\ $$
Answered by Eulerian last updated on 28/Jan/22
$$\: \\ $$$$\:\boldsymbol{\mathrm{Solution}}: \\ $$$$\:\left(\mathrm{10}−\mathrm{r}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} \:=\:\mathrm{r}^{\mathrm{2}} \\ $$$$\:\mathrm{25}\:=\:\mathrm{20r}−\mathrm{100} \\ $$$$\:\mathrm{r}\:=\:\frac{\mathrm{125}}{\mathrm{20}}\:=\:\frac{\mathrm{25}}{\mathrm{4}}\:\mathrm{cm} \\ $$