Question-213550

Question Number 213550 by mr W last updated on 08/Nov/24

Commented by mr W last updated on 08/Nov/24

$${semicircle} \\ $$

Answered by A5T last updated on 08/Nov/24

Commented by A5T last updated on 08/Nov/24

$$\frac{{s}−\mathrm{3}}{\mathrm{2}}={r}−\mathrm{3}\Rightarrow{s}=\mathrm{2}{r}−\mathrm{3} \\ $$$$\frac{{t}−\mathrm{6}}{\mathrm{2}}={r}−\mathrm{6}\Rightarrow{t}=\mathrm{2}{r}−\mathrm{6} \\ $$$$\left({t}−\mathrm{6}\right)^{\mathrm{2}} +\left({s}−\mathrm{3}\right)^{\mathrm{2}} =\left(\mathrm{2}{r}\right)^{\mathrm{2}} =\mathrm{4}{r}^{\mathrm{2}} \\ $$$$\Rightarrow\left(\mathrm{2}{r}−\mathrm{12}\right)^{\mathrm{2}} +\left(\mathrm{2}{r}−\mathrm{6}\right)^{\mathrm{2}} =\mathrm{4}{r}^{\mathrm{2}} \\ $$$$\Rightarrow{r}^{\mathrm{2}} −\mathrm{18}{r}+\mathrm{45}=\mathrm{0}\Rightarrow{r}=\mathrm{3}\:{or}\:\mathrm{15} \\ $$$${t}−\mathrm{6}>\mathrm{0}\Rightarrow{r}=\mathrm{15}\Rightarrow\mathrm{2}{r}=\mathrm{30} \\ $$

Commented by mr W last updated on 08/Nov/24

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Answered by Spillover last updated on 09/Nov/24

$$ \\ $$R²=[R -6]²+ [R -3]²
R² -12R +36 + R² -6R +9
R²=2R² -18R +45 R² -18R +45=0
R=[18+[324 – 180]½]/2

R=[18+12]/2=15
EF=[15+15]=30

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