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Question Number 148532 by cherokeesay last updated on 28/Jul/21

Answered by mr W last updated on 29/Jul/21

Commented by mr W last updated on 29/Jul/21

$$R=6cm$$$$DG=\sqrt{2}r+r=R$$$$\Rightarrow r=\frac{R}{\sqrt{2}+1}=(\sqrt{2}-1)R$$$$DF=\frac{R}{\sqrt{2}}=\frac{\sqrt{2}R}{2}$$$$CF=DF-\sqrt{2}r=\frac{\sqrt{2}R}{2}-(2-\sqrt{2})R=(\frac{3\sqrt{2}}{2}-2)R$$$$AF=\sqrt{r^2-{(\frac{3\sqrt{2}}{2}-2)}^2{R}^2}$$$$AF=R\sqrt{{(\sqrt{2}-1)}^2-{(\frac{3\sqrt{2}}{2}-2)}^2}$$$$AF=\frac{1}{2}R\sqrt{16\sqrt{2}-22}$$$$AB=2AF=\sqrt{16\sqrt{2}-22}R\approx 0.792R\approx 4.753$$

Commented by cherokeesay last updated on 29/Jul/21

$$Iwouldalsoliketosharemysolution!$$$$thankyoualotmrW!$$

Commented by Tawa11 last updated on 29/Jul/21

$$\mathrm{Nice}\mathrm{sir}.\mathrm{Thanks}.$$

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