Category: Geometry

Question Number 64246 by mr W last updated on 16/Jul/19 Answered by mr W last updated on 16/Jul/19 $${x}=\frac{\mathrm{1}}{\mathrm{sin}\:\theta} \\ $$$$\mathrm{tan}\:\frac{\theta}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{sin}\:\theta=\frac{\mathrm{2}×\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }=\frac{\mathrm{4}}{\mathrm{5}} \\…

Question Number 64097 by ajfour last updated on 13/Jul/19 Commented by ajfour last updated on 13/Jul/19 $${Find}\:{side}\:{length}\:\boldsymbol{{s}}\:{of}\:{equal}\:{sided} \\ $$$${hexagon}\:{inscribed}\:{in}\:{ellipse}\:{of} \\ $$$${parameters}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}. \\ $$ Answered by…

Question Number 129547 by Adel last updated on 16/Jan/21 $$\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{conditions}\:\mathrm{is}\:\mathrm{true}\: \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{folowing}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{verticale} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{a}_{\mathrm{1}} \mathrm{x}+\mathrm{b}_{\mathrm{1}} \mathrm{y}+\mathrm{c}_{\mathrm{1}} =\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{a}_{\mathrm{2}}…

Question Number 63981 by ajfour last updated on 11/Jul/19 Answered by mr W last updated on 11/Jul/19 $$\left[\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} −{b}^{\mathrm{2}} }+\sqrt{\left({a}−{r}\right)^{\mathrm{2}} −{r}^{\mathrm{2}} }\right]^{\mathrm{2}} =\left({b}+{r}\right)^{\mathrm{2}} −\left({b}−{r}\right)^{\mathrm{2}}…

Question Number 63750 by Tawa1 last updated on 08/Jul/19 Commented by Prithwish sen last updated on 08/Jul/19 $$\mathrm{perimeter}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{A}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\pi\mathrm{r}\:\mathrm{unit} \\ $$$$\mathrm{perimeter}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{B}\:=\:\mathrm{2}\pi\mathrm{r}\:\mathrm{unit} \\ $$$$\mathrm{Circle}\:\mathrm{A} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{covers}\:\frac{\mathrm{2}}{\mathrm{3}}\pi\mathrm{r}\:\mathrm{in}\:\mathrm{1}\:\mathrm{time} \\…