Category: Geometry

Question Number 218886 by Spillover last updated on 17/Apr/25 Answered by mr W last updated on 17/Apr/25 Commented by Spillover last updated on 17/Apr/25 $${perfect}…

Question Number 218813 by Spillover last updated on 15/Apr/25 Answered by nikif99 last updated on 15/Apr/25 Commented by Spillover last updated on 16/Apr/25 $${great}\:{work}.{thanks}\: \…

Question Number 218676 by Spillover last updated on 14/Apr/25 Answered by mr W last updated on 14/Apr/25 $$\cos \theta =\frac{R-r}{R+r}=1-2{\sin }^2\frac{\theta }{2}$$$$\Rightarrow \sin \frac{\theta }{2}=\sqrt{\frac{r}{R+r}}$$$$x=2R\sin \frac{\theta }{2}=2R\sqrt{\frac{r}{R+r}}✓$$…

Question Number 218737 by Spillover last updated on 14/Apr/25 Answered by Spillover last updated on 16/Apr/25 Answered by Spillover last updated on 16/Apr/25 Terms of…

Question Number 218739 by Spillover last updated on 14/Apr/25 Answered by A5T last updated on 15/Apr/25 $$\mathrm{AB}=\mathrm{c};\mathrm{BC}=\mathrm{a};\mathrm{CA}=\mathrm{b};\mathrm{AF}={\mathrm{h}}_{\mathrm{a}}$$$$\mathrm{AF}\mathrm{\perp }\mathrm{BC};\mathrm{BG}\mathrm{\perp }\mathrm{DC};\mathrm{DH}\mathrm{\perp }\mathrm{BC}$$$$\mathrm{S}_{\bigtriangleup\mathrm{ABC}} =\frac{\mathrm{ah}_{\mathrm{a}} }{\mathrm{2}}\Rightarrow\mathrm{h}_{\mathrm{a}} =\frac{\mathrm{2S}_{\bigtriangleup\mathrm{ABC}} }{\mathrm{a}}…