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Question Number 201581 by cortano12 last updated on 09/Dec/23

Answered by mr W last updated on 09/Dec/23

Commented by mr W last updated on 09/Dec/23

$$R=\frac{8+2}{2}=5$$$$r=OM=\sqrt{8\times 2}=4$$$$letx=\frac{PQ}{2}$$$$\sqrt{R^2-x^2}+\sqrt{r^2-x^2}=R$$$$r^2=2R\sqrt{r^2-x^2}$$$$\Rightarrow x=r\sqrt{1-\frac{r^2}{4R^2}}$$$$\Rightarrow PQ=2r\sqrt{1-\frac{r^2}{4R^2}}$$$$=2\times 4\sqrt{1-\frac{4^2}{4\times 5^2}}=\frac{8\sqrt{21}}{5}\approx 7.332$$

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