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Question Number 17901 by chux last updated on 12/Jul/17

Commented by chux last updated on 12/Jul/17

$$\mathrm{find}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{big}\mathrm{and}$$$$\mathrm{small}\mathrm{circle}$$

Commented by chux last updated on 12/Jul/17

$$\mathrm{yes},\mathrm{they}\mathrm{are}$$

Answered by mrW1 last updated on 12/Jul/17

$$2(\mathrm{R}-\mathrm{r})=90...\left(\mathrm{i}\right)$$$${(\mathrm{R}-50)}^2={\mathrm{r}}^2-{(\mathrm{R}-\mathrm{r})}^2...\left(\mathrm{ii}\right)$$$$\left(\mathrm{i}\right):$$$$\mathrm{R}=45+\mathrm{r}$$$$\left(\mathrm{ii}\right):$$$${(45+\mathrm{r}-50)}^2={\mathrm{r}}^2-{\left(45\right)}^2$$$${(\mathrm{r}-5)}^2={\mathrm{r}}^2-{45}^2$$$${\mathrm{r}}^2-10\mathrm{r}+25={\mathrm{r}}^2-{45}^2$$$$10\mathrm{r}=2050$$$$\mathrm{r}=205$$$$\mathrm{R}=45+205=250$$

Commented by chux last updated on 12/Jul/17

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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