Category: Geometry

Question Number 30862 by ajfour last updated on 27/Feb/18 Answered by mrW2 last updated on 27/Feb/18 $$\frac{{a}}{\mathrm{sin}\:{A}}=\frac{{b}}{\mathrm{sin}\:{B}}=\frac{{c}}{\mathrm{sin}\:{C}}=\frac{\mathrm{1}}{\lambda}=\mathrm{2}{R}=\frac{{abc}}{\mathrm{2}\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}} \\ $$$$\frac{{BQ}}{\mathrm{sin}\:\left({C}−\theta\right)}=\frac{{CQ}}{\mathrm{sin}\:\theta}=\frac{{BC}}{\mathrm{sin}\:\left(\pi−\theta−{C}+\theta\right)} \\ $$$$\frac{{BQ}}{\mathrm{sin}\:\left({C}−\theta\right)}=\frac{{CQ}}{\mathrm{sin}\:\theta}=\frac{{a}}{\mathrm{sin}\:{C}} \\ $$$$\Rightarrow{BQ}=\frac{\mathrm{sin}\:\left({C}−\theta\right)}{\mathrm{sin}\:{C}}×{a} \\ $$$$\Rightarrow{CQ}=\frac{\mathrm{sin}\:\theta}{\mathrm{sin}\:{C}}×{a}…

Question Number 30808 by 33 last updated on 26/Feb/18 Answered by mrW2 last updated on 26/Feb/18 Commented by mrW2 last updated on 26/Feb/18 $${x}_{\mathrm{1}} =\mathrm{2}{a}\:\mathrm{cos}\:\theta…

Question Number 161742 by mr W last updated on 21/Dec/21 Commented by mr W last updated on 21/Dec/21 $${find}\:{the}\:{radii}\:{of}\:{the}\:{circles}\:{inside} \\ $$$${the}\:{big}\:{quater}\:{circle}. \\ $$ Answered by…

Question Number 161424 by cherokeesay last updated on 17/Dec/21 Answered by aleks041103 last updated on 17/Dec/21 $$\left({R}−\mathrm{2}\right)^{\mathrm{2}} +\left({R}−\mathrm{4}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$${R}^{\mathrm{2}} −\mathrm{4}{R}+\mathrm{4}+{R}^{\mathrm{2}} −\mathrm{8}{R}+\mathrm{16}={R}^{\mathrm{2}} \\ $$$${R}^{\mathrm{2}}…

Question Number 95830 by I want to learn more last updated on 27/May/20 Answered by behi83417@gmail.com last updated on 28/May/20 $$\mathrm{4s}+\frac{\mathrm{16}^{\mathrm{2}} }{\mathrm{2}}=\mathrm{16}^{\mathrm{2}} \Rightarrow\mathrm{s}=\frac{\mathrm{16}^{\mathrm{2}} }{\mathrm{8}}=\mathrm{32} \\…