Category: Geometry

Question Number 181852 by mnjuly1970 last updated on 01/Dec/22 Answered by mr W last updated on 01/Dec/22 $$\frac{a}{\sin \alpha }=\frac{b}{\sin \beta }=\frac{c}{\sin \gamma }=2R$$$$S_{ABC}=\frac{bc\sin \alpha }{2}=2R^2\sin \alpha \sin \beta \sin \gamma$$$${S}_{{ABC}} ={R}\left(\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta+\mathrm{sin}\:\gamma\right){r}…

Question Number 181834 by mr W last updated on 01/Dec/22 Commented by mr W last updated on 01/Dec/22 $$anunsolvedoldquestion$$ Terms of Service Privacy…

Question Number 181812 by HeferH last updated on 01/Dec/22 Answered by mr W last updated on 01/Dec/22 $$\sin 30°=\frac{\sin (2\alpha +30°)}{2\cos \alpha }$$$$\sin (2\alpha +30°)=\cos \alpha =\sin (90°-\alpha )$$$$2\alpha +30°=90°-\alpha \Rightarrow \alpha =20°$$$${or} \…

Question Number 181766 by HeferH last updated on 30/Nov/22 Answered by som(math1967) last updated on 30/Nov/22 $$letradiusofinnercircle=r$$$$\frac{CI}{r}=cosec20\Rightarrow CI=rcosec20$$$$c=rcot30+rcot40$$$$=r\left(\frac{cos30sin40+cos40sin30}{sin30sin40}\right)$$$$={r}\left(\frac{\mathrm{2}{sin}\mathrm{70}}{\mathrm{2}{sin}\mathrm{20}{cos}\mathrm{20}}\right)…

Question Number 50674 by mr W last updated on 18/Dec/18 $$Findthemaximumareaofatriangle$$$$inscribedinanellipsewithparameters$$$$aandb.$$ Commented by ajfour last updated on 18/Dec/18 Commented…