Question Number 87759 by M±th+et£s last updated on 06/Apr/20
Commented by mr W last updated on 06/Apr/20
$$\Delta{DEC}\sim\Delta{ECF}\sim\Delta{PFE} \\ $$$$\frac{{r}_{{z}} }{{EF}}=\frac{{r}_{{y}} }{{FC}}=\frac{{r}_{{x}} }{{CE}}={k},\:{say} \\ $$$$\Rightarrow{CE}=\frac{{r}_{{x}} }{{k}} \\ $$$$\Rightarrow{FC}=\frac{{r}_{{y}} }{{k}} \\ $$$$\Rightarrow{EF}=\frac{{r}_{{z}} }{{k}} \\ $$$${CE}^{\mathrm{2}} +{FC}^{\mathrm{2}} ={EF}^{\mathrm{2}} \\ $$$$\Rightarrow\frac{{r}_{{x}} ^{\mathrm{2}} }{{k}^{\mathrm{2}} }+\frac{{r}_{{x}} ^{\mathrm{2}} }{{k}^{\mathrm{2}} }=\frac{{r}_{{z}} ^{\mathrm{2}} }{{k}^{\mathrm{2}} } \\ $$$$\Rightarrow{r}_{{x}} ^{\mathrm{2}} +{r}_{{y}} ^{\mathrm{2}} ={r}_{{z}} ^{\mathrm{2}} \\ $$$$\Rightarrow\pi{r}_{{x}} ^{\mathrm{2}} +\pi{r}_{{y}} ^{\mathrm{2}} =\pi{r}_{{z}} ^{\mathrm{2}} \\ $$$$\Rightarrow{area}\:{circle}\:{x}+{area}\:{circle}\:{y}={area}\:{circle}\:{z} \\ $$
Commented by M±th+et£s last updated on 06/Apr/20
$${thank}\:{you}\:{sir} \\ $$