Category: Geometry

Question Number 182149 by Acem last updated on 05/Dec/22 Commented by Acem last updated on 05/Dec/22 $$Find\alpha$$ Answered by HeferH last updated on…

Question Number 182103 by mr W last updated on 04/Dec/22 Commented by mr W last updated on 04/Dec/22 $$findthesmallestareaofinscribed$$$$equilateraltriangleinthegiven$$$$trianglewithsides3,5,7.$$…

Question Number 182078 by Acem last updated on 04/Dec/22 Answered by mr W last updated on 05/Dec/22 $$\frac{\sin 30}{\sin (30-\theta )}=\frac{\sin (30+\theta )}{\sin \theta }$$$$\frac{\sin \theta }{2}=\frac{(\cos \theta +\sqrt{3}\sin \theta )(\cos \theta -\sqrt{3}\sin \theta )}{4}$$$$\mathrm{2}\:\mathrm{sin}\:\theta=\mathrm{cos}^{\mathrm{2}} \:\theta−\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} \:\theta \…

Question Number 182066 by HeferH last updated on 03/Dec/22 Answered by a.lgnaoui last updated on 04/Dec/22 $$△\mathrm{ABC}$$$$\mathrm{ABcos}2\mathrm{x}+\mathrm{BCcos}\mathrm{x}=\mathrm{ADcos}3\mathrm{x}+\mathrm{CDcos}4\mathrm{x}$$$$\frac{\sin 2\mathrm{x}}{\mathrm{BC}}=\frac{\mathrm{sinx}}{\mathrm{AB}}\left(1\right)\frac{\sin 3\mathrm{x}}{\mathrm{CD}}=\frac{\sin 4\mathrm{x}}{\mathrm{AD}}\left(2\right)$$$$\mathrm{ABsin}2\mathrm{x}=\mathrm{BCsin}\mathrm{x}\mathrm{AD}\sin 3\mathrm{x}=\mathrm{CDsin}4\mathrm{x}$$$$\mathrm{AB}=\frac{\mathrm{BCsin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{2x}}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{CD}=\frac{\mathrm{ADsin}\:\mathrm{3x}}{\mathrm{sin}\:\mathrm{4x}}…

Question Number 116466 by mr W last updated on 04/Oct/20 Commented by mr W last updated on 04/Oct/20 $$R=radiusofbigcircles$$$$r=radiusofsmallcircles$$$$let\lambda =\frac{r}{R}$$$$\mathrm{cos}\:\alpha=\frac{{R}}{{R}+{r}}=\frac{\mathrm{1}}{\mathrm{1}+\lambda}…