Category: Geometry

Question Number 159005 by Tawa11 last updated on 11/Nov/21 Answered by ajfour last updated on 12/Nov/21 $$s=2r\sin \alpha$$$$p=r\sin 2\alpha$$$$\cos \beta =\frac{35/2}{r}=\frac{7}{8};\sin \beta =\frac{\sqrt{15}}{8}$$$$\frac{\sin (90°-\alpha )}{27}=\frac{\sin (3\alpha +\beta )}{p}$$$$\mathrm{20sin}\:\mathrm{2}\alpha\mathrm{cos}\:\alpha=\mathrm{27sin}\:\left(\mathrm{3}\alpha+\beta\right)…

Question Number 158924 by ajfour last updated on 10/Nov/21 Commented by ajfour last updated on 10/Nov/21 $$a,b,careslantedgesofouter$$$$tetrahedron.Findminimum$$$$volumeofinnertetrahedron$$$$whoseverticeslieonfacesof$$$${outer}\:{one}\:{when}\:{the}\:{outer}\:{one}…

Question Number 158749 by ajfour last updated on 08/Nov/21 Commented by ajfour last updated on 08/Nov/21 $$FindextremevaluesofR.$$ Answered by mr W last updated…

Question Number 27627 by Rasheed.Sindhi last updated on 11/Jan/18 Commented by Rasheed.Sindhi last updated on 11/Jan/18 $$\mathrm{Given}\mathrm{a}\mathrm{circle}\mathrm{of}\mathrm{radius}\mathrm{r}.\mathrm{AB}\mathrm{\&}\mathrm{CD}$$$$\mathrm{are}\mathrm{two}\mathrm{chords}\mathrm{intersecting}\mathrm{at}\mathrm{E}$$$$\mathrm{OX}\mathrm{and}\mathrm{OY}\mathrm{are}\mathrm{respective}\mathrm{distances}$$$$\mathrm{of}\mathrm{chords}\mathrm{CD}\mathrm{and}\mathrm{AB}\mathrm{from}\mathrm{center}$$$$\mathrm{of}\:\mathrm{the}\:\mathrm{circle}.…

Question Number 158622 by ajfour last updated on 06/Nov/21 Commented by ajfour last updated on 06/Nov/21 $$Findmaximumsidelength$$$$ofinscribedsquare\left(s_{max}\right).$$ Answered by mr…