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Category: Geometry

Question-163143

Question Number 163143 by amin96 last updated on 04/Jan/22 Commented by HongKing last updated on 04/Jan/22 $$\mathrm{r}^{\mathrm{2}} \:=\:\mathrm{r}\:+\:\mathrm{2021}\:+\:\mathrm{2021}^{\mathrm{2}} \\ $$$$\mathrm{r}^{\mathrm{2}} \:-\:\mathrm{r}\:-\:\mathrm{2021}^{\mathrm{2}} \:-\:\mathrm{2021}\:=\:\mathrm{0} \\ $$$$\mathrm{r}\:=\:-\:\mathrm{2021}\:;\:\mathrm{2022}\:\Rightarrow\:\mathrm{r}\:=\:\mathrm{2022}\:\checkmark \\…

Question-97557

Question Number 97557 by Power last updated on 08/Jun/20 Answered by mr W last updated on 08/Jun/20 $$\angle{CBE}=\angle{EBD}=\theta=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}−\alpha\right) \\ $$$$\Rightarrow\mathrm{2}\theta=\frac{\pi}{\mathrm{2}}−\alpha \\ $$$${BD}=\mathrm{2}{r}\:\mathrm{sin}\:\alpha \\ $$$${EB}=\frac{\mathrm{2}{r}}{\mathrm{cos}\:\theta} \\…

Question-162481

Question Number 162481 by mnjuly1970 last updated on 29/Dec/21 Answered by mr W last updated on 29/Dec/21 $${length}\:{of}\:{base}\:={h} \\ $$$$\mathrm{tan}\:\alpha=\frac{{b}}{{h}} \\ $$$$\mathrm{tan}\:\mathrm{2}\alpha=\frac{{b}+{a}}{{h}} \\ $$$$\mathrm{tan}\:\mathrm{3}\alpha=\frac{{b}+{a}+{x}}{{h}} \\…