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Category: Geometry

Question-166676

Question Number 166676 by ajfour last updated on 24/Feb/22 Answered by ajfour last updated on 24/Feb/22 $${R}\mathrm{sin}\:\theta+\mathrm{2}{r}={R} \\ $$$$\mathrm{sin}\:\theta=\frac{{r}}{{R}−{r}} \\ $$$$\Rightarrow\:\:{Rr}=\left({R}−\mathrm{2}{r}\right)\left({R}−{r}\right) \\ $$$$\Rightarrow\:\:{R}^{\mathrm{2}} −\mathrm{4}{rR}+\mathrm{2}{r}^{\mathrm{2}} =\mathrm{0}…

Question-166640

Question Number 166640 by cherokeesay last updated on 23/Feb/22 Answered by som(math1967) last updated on 24/Feb/22 $${Area}\:{with}\:{circle} \\ $$$$=\mathrm{2}×\left\{\frac{\pi}{\mathrm{6}}×\mathrm{4}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}×\mathrm{4}^{\mathrm{2}} \right\}{cm}^{\mathrm{2}} \\ $$$$=\left(\frac{\mathrm{16}\pi}{\mathrm{3}}\:−\mathrm{4}\sqrt{\mathrm{3}}\right){cm}^{\mathrm{2}} \: \\…